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Mĩ thuật thế giới thời kì tiền sử
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BÀI 9: HÀNH TRANG CUỘC SỐNG Tiết 96 THỰC HÀNH TIẾNG VIỆT SỬ DỤNG PHƯƠNG TIỆN PHI NGÔN NGỮ (tiếp theo) I. MỤC TIÊU 1. Năng lực a. Năng lực chung: - Năng lực thu thập thông tin liên quan đến văn bản - Năng lực đọc - hiểu văn bản - Năng lực trình bày suy nghĩ - Năng lực tự học, tạo lập văn bản. - Ứng dụng CNTT linh hoạt qua các phần mềm hỗ trợ b. Năng lực đặc thù: Bài học góp phần phát triển năng lực văn học và năng lực ngôn ngữ: - HS nhận biết và sử dụng kết hợp giữa phương tiên ngôn ngữ và phương tiện phi ngôn ngữ như một số loại biểu đồ, sơ đồ cơ bản (biểu đồ tròn, biểu đồ Venn, biểu đồ thời gian, sơ đồ cây…) 2. Phẩm chất Có ý thức làm chủ bản thân, đóng góp tích cực cho bài học. II. THIẾT BỊ DẠY HỌC VÀ HỌC LIỆU 1. Thiết bị dạy học: Máy tính bỏ túi, máy chiếu, Laptop, Giấy bìa A3; bút dạ, nam châm bảng; phấn màu 2. Học liệu: - Một số mảnh ghép hình, sơ đồ, lược đồ về biển giao thông, khu du lịch, chương trình học đại học… III. TIẾN TRÌNH DẠY HỌC Hoạt động 1: KHỞI ĐỘNG a. Mục tiêu: Tạo tâm thế thoải mái và gợi dẫn cho học sinh về nội dung bài học b. Nội dung: Trò chơi ghép hình với tên gọi: Hình nào tên đó c. Sản phẩm: - Mỗi nhóm tạo được một bức ghép hình hoàn chỉnh. - HS nêu đúng ý nghĩa, chức năng của tấm hình d. Tổ chức thực hiện: Bước 1: GV giao nhiệm vụ học tập + Phân lớp thành 4 nhóm + Mỗi nhóm nhận một số mảnh ghép (trong túi bất kì, các hình khác nhau) + 1 bạn được xem trước hình ảnh gốc (trong 1 giây) ghi nhớ và cùng đội lắp ghép lại như hình Bước 2: Thực hiện nhiệm vụ - Các nhóm cùng có 3 phút để hoàn thành bức hình gốc, các thành viên cùng phối hợp thực hiện VD: Hình 1 Hình 2 Hình 3 Hình 4 Bước 3: Báo cáo kết quả * Trình bày và nêu ý nghĩa của bức hình (1 phút) - Bức 1: Biển báo giao thông đường bộ (Các biển cấm) + Giúp người đi đường thực hiện đúng luật giao thông - Bức 2: Quy trình sử dụng khẩu trang + Giúp biết cách sử dụng đúng, hạn chế tối đa lây nhiễm bệnh - Bức 3: Sơ đồ tuyến đường xe buýt của bạn + Giúp người đi đường tìm đúng tuyến nhanh nhất - Bức 4: Lược đồ thành phố Hà Nội + Giúp mọi người có hiểu biết về địa giới hành chính, xác định được vị trí địa bàn sinh sống và làm việc. Bước 4: Kết luận, nhận định - HS đánh giá nhóm nào nhanh nhất, hoàn chỉnh nhất và nêu đầy đủ ý nghĩa nhất. - GV: Công bố đáp án, điểm số và biểu dương đội xuất sắc. =>Kết luận: Các hình ảnh này đều cung cấp thông tin cho người đọc, nhận biết những quy định, cách thức, vị trí, để hiểu đúng, hiểu rõ nội dung hơn nữa. Đây là cách trình bày trực quan, dễ hiểu, dễ nhớ, dễ thực hiện Hoạt động 2: HÌNH THÀNH KIẾN THỨC a. Mục tiêu: - Nhận biết các yếu tố, các đặc điểm của một sơ đồ - Hiểu được nội dung thông tin của văn bản đó - Nêu được tác dụng của sơ đồ - Vận dụng để giải quyết bài tập b. Nội dung: Bài 1 -SGK trang 111 c. Sản phẩm: - HS nêu được tác dụng của các PT phi ngôn ngữ d. Tổ chức thực hiện: Hoạt động của GV Dự kiến sản phẩm Hoạt động 1: Bài tập 1 Bước 1. Giao nhiệm vụ học tập - Quan sát sơ đồ - Nhận xét các vấn đề sau: Nhóm 1: Nhận xét sự thay đổi phương diện Tài chính Nhóm 2: Tìm sự thay đổi về phương diện Sở thích Nhóm 3: Nhận xét thay đổi về phương diện Cống hiến Nhóm 4: Tìm sự thay đổi về phương diện Công việc Nhóm 5: Nhận xét thay đổi về phương diện Gia đình - Nêu nội dung của sơ đồ và tác dụng của các phương tiện phi ngôn ngữ trong sơ đồ. Bước 2. Thực hiện nhiệm vụ - Các nhóm thảo luận trao đổi trong 3 phút - Đại diện nhóm trả lời trong 1 phút; nhóm khác có thể bổ sung thông tin - Cá nhân tự ghi chép lại nội dung. Bước 3. Báo cáo, thảo luận Học sinh chia sẻ bài làm và báo cáo phần tìm hiểu Bước 4. Kết luận, nhận định - HS biết đọc nội dung của biểu đồ, nêu đầy đủ ngắn gọn thông tin - GV đánh giá nhóm và đại diện nhóm, rút KN Hoạt động 2: Bài tập 2 Bước 1. Giao nhiệm vụ học tập + Vẽ sơ đồ biểu thị các yếu tố: Thời gian, sự kiện, thành tựu, mong muốn, những ngã rẽ…Biểu thị được các lĩnh vực trong cuộc sống theo lựa chọn cá nhân… + Trình bày nội dung bản sơ đồ đó trước nhóm/ lớp (trên các slide- PP/bảng/ hoặc trên giấy vẽ A4) Bước 2. Thực hiện nhiệm vụ - Bài làm theo hình thức cá nhân ( vì là cuộc đời riêng mỗi người) - Thời gian thực hiện: 7 phút (gồm vẽ và trình bày) Bước 3. Báo cáo, thảo luận - HS trình bày sản phẩm cá nhân: Hình thức sơ đồ có thể tương tự như bài 1, hoặc biểu đồ thời gian (trang 112) có thể chia theo nhóm hình thức giống nhau Bước 4. Kết luận, nhận định - HS có thể nhận xét, tìm đại diện làm tốt nhất của nhóm mình. - GV nhận xét bài làm, tinh thần làm việc để rút KN Bài tập 1: Nhóm 1: Tài chính có mục tiêu rõ ràng, lâu dài, sử dụng vào những việc lớn trong cuộc sống, với kế hoạch từ năm thứ 10 (mua nhà) và tích lũy tài sản ngày càng lớn vào năm thứ 15 (sổ TK 2 tỉ) Nhóm 2: Sở thích cá nhân có sự thay đổi từ chơi bóng (năm thứ 5) du lịch (năm thứ 10) và vẽ tranh (năm thứ 15)- đa dạng, phong phú theo sở trưởng. Nhóm 3: Càng ngày việc làm từ thiện càng phát triển, có cống hiến nhiều cho cộng đồng (tăng dần theo giai đoạn 5 năm) Nhóm 4: Công việc ngày càng tiến bộ, có mục tiêu rõ ràng, phát triển bền vững Nhóm 5: Xây dựng gia đình khi sự nghiệp đã vững vàng, thời điểm thuận lợi. Nhận xét chung: Sơ đồ cho thấy bản kế hoạch rất rõ ràng, có mục tiêu cụ thể, có tính tiến triển- khả thi và rất chặt chẽ. Giúp người lập KH tập trung phấn đấu xây dựng cho sự nghiệp, tận hưởng cuộc sống và hài hòa mọi mặt. (toàn diện) Phương tiện phi ngôn ngữ được sử dụng hợp lí, ngắn gọn, dễ hiểu… Bài tập 2: Một bản vẽ minh họa: TÔI TRONG TƯƠNG LAI Hoạt động 3: Luyện tập a. Mục tiêu: - Tăng cường kĩ năng giải quyết vấn đề + Xác định được mục đích giao tiếp của văn bản + Lựa chọn các thông tin cần trực quan thành sơ đồ + Lựa chọn loại sơ đồ, biểu đồ phù hợp - Rèn năng lực diễn đạt, trình bày; Có thể ứng dụng công nghệ tin học vào thực hành b. Nội dung: - Thiết kế một biểu đồ hoặc sơ đồ dựa trên thông tin từ đoạn trích SGK (trang 111) - Quan sát và nêu nội dung, tác dụng của biểu đồ cơ cấu dân số Yên Bái c. Sản phẩm: - Bài 3: Bản thiết kế Sơ đồ tư duy/ sơ đồ cây (từ văn bản bằng ngôn ngữ chuyển hóa thành phi ngôn ngữ) - Từ văn bản phi ngôn ngữ (biểu đồ) để đọc thông tin d. Tổ chức thực hiện: B1: Chuyển giao nhiệm vụ - Lớp chia 4 nhóm: + Nhóm 1, 2 (Bài 3): Thảo luận phương án, thiết kế một sơ đồ phù hợp dựa trên thông tin từ đoạn trích (trang 111) + Nhóm 3,4: Quan sát và nêu nội dung, tác dụng của biểu đồ cơ cấu dân số Yên Bái (trang 112), tìm công cụ phần mềm để làm biểu đồ tương tự. - Đại diện nhóm trình bày sản phẩm B2: Thực hiện nhiệm vụ - Đọc kĩ yêu cầu nhiệm vụ. - Thảo luận và phân công nhiệm vụ cho thành viên - Thời gian thực hiện 5 phút/ trình bày 2 phút B3: Báo cáo thảo luận Nhóm 1,2 - Bài 3: Trình bày bằng sơ đồ tư duy hoặc sơ đồ cây (tham khảo bản vẽ trên PP) Nhóm 3,4- Nêu nội dung đọc được từ biểu đồ - Nêu tác dụng và nhận xét: + Người đọc dễ tra cứu thông tin, biết cách so sánh + Các số liệu chính xác, đầy đủ, thông tin rõ ràng + Hình thức khoa học, đúng kiểu dạng phù hợp với yêu cầu, có tính thẩm mĩ - Một số ứng dụng để vẽ biểu đồ: Phần mềm PP; Dia, OrgChatting… Gợi ý: B4: Kết luận, nhận định - Nhóm 1,2: nhận xét sản phẩm nhóm 3, 4 - Nhóm 3,4: nhận xét sản phẩm nhóm 1, 2 - GV nhận xét chung; nêu kết luận và rút KN Hoạt động 4: Hướng dẫn học sinh tự học ở nhà 1. Bài cũ - Hoàn thiện bài tập 2. Bài mới Chuẩn bị bài viết: viết bài luận về bản thân - Đọc bài viết tham khảo - Tìm hiểu các bước viết bài luận về bản thânBài 1: Một số thể loại mĩ thuậtTẠO CÂU HỎI TRẮC NGHIỆM VỀ MỘT SỐ THỂ LOẠI MĨ THUẬTTẠO CÂU HỎI TRẮC NGHIỆM MỘT SỐ THỂ LOẠI MĨ THUẬTIntroduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: • Free-falling objects do not encounter air resistance. • All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs • Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 • (-8.00 m/s2) • d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) • d (16.0 m/s2) • d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s2) • (4.10 s)2 d = (0 m) + ½ • (6.00 m/s2) • (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: • An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. • If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2 -8.52 m = (-4.9 m/s2) • (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 •(-9.8m/s2) •d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d (-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) • d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.Melody. Melody is a musical element that determines the sequence of tones on the staff. There are different directions (up, down, skip, step/scale and repeat/even)The up and down movement of its pitches conveys tension and release, expectation and arrival. This is the melodic curve or line. A melody moves by small intervals called steps or by larger ones called leaps. A step is the interval between two adjacent tones in the do-re-mi scale (from do to re, re to mi, etc.)• Any interval larger than a step is a leap (do to mi, for example). Besides moving up or down by step or leap, a melody may simply repeat the same note. The Philippine Flag Our country is officially identified through our flag. The Philippine flag has three colors: white, blue, and red. White signifies purity; blue means hope and peace; and red denotes bravery. The three stars symbolize the three big groups of islands of our country-the Luzon, Visayas, and Mindanao. The eight rays of the sun signify the eight provinces that first revolted against the Spaniards. These are Bulacan, Pampanga, Tarlac, Nueva Ecija, Laguna, Batangas, Manila, and Cavite. We respect our flag to show that we respect our country. We should not treat it like an ordinary cloth because it symbolizes our country. An old flag should be burned and not be used as a rag. Title: National Hero Body text: Dr. Jose Rizal was from a middle-class family from Calamba, Laguna. He is regarded as a genius who fought the Spaniards through his writings, especially the novels "Noli Me Tangere" and "El Filibusterismo." The two novels exposed the anomalies and wrongdoings of the Spanish government against the Filipino people. He wrote the poem "Mi Ultimo Adios" the eve before his execution in Bagumbayan (now known as Rizal Park). National Fruit A mango is sour when it is green, but very sweet when it is ripe. This heart-shaped fruit symbolizes the kindness of the Filipinos. It has a big tree that bears fruits abundantly during summer. National Animal A carabao is a model of hard work and industry. It is the best companion of farmers in the field. It is black and looks like a tamaraw. A carabao is a very strong animal in terms of work. It symbolizes the Filipinos as hardworking and patient. National Bird The Philippine eagle, also known as haribon, stands over 5 feet (1.6 m) tall. It has a large, sharp, and aggressive beak and has powerful talons. Philippine eagles are excellent hunters, and live in tropical rainforests. These eagles lay just one or two eggs each year. National Tree The narra is a hardy tree that grows big and is found mainly in the Bicol Region, Mindanao, and Cagayan Valley forests. Most of the desks and tables in schools are made of narra. It signifies the strong personality of Filipinos in facing trials in life. National Flower The sampaguita has white, star-shaped petals with a sweet fragrance. It is made into garlands, which are given to visitors and special persons on occasions. It signifies purity and among Filipino women. National Fish Bangus or milkfish is our national fish. It grows in ponds or freshwater and tastes delicious. Its white, shiny scales signify our beautiful country. National Dance Cariñosa is a dance of love using a handkerchief and a fan. It symbolizes the true love expressed by Filipinos. National House A nipa hut is a small but beautiful house made from bamboo and sawali or cogon leaves. Filipinos used this kind of house during the olden times. At present, there are still people using this as a dwelling place, but most of the time, they use it as a rest place or cottage. National Costume Barong Tagalog is the national costume for Filipino men. It is made from pineapple fiber or other native materials. Filipinos wear this on special occasions such as formal events or weddings. Baro at Saya is the national dress for Filipino women. Most of them are made from jusi or pineapple fiber and other native materials. This dress shows the gracefulness of Filipino women. National Leaf Our national leaf is a palm tree. It is wide and narrow like an open fan. Farmers use this to protect their crops from the harsh sunlight and rain. It grows like a tree with thorns in its body. National Language Our national language is Filipino, which is based in Tagalog. Through the efforts of former President Manuel L. Quezon (known as the "Father of the National Language"), Filipino was widely disseminated and is now used in all parts of the country. With this, Filipinos in different cultures and native tongues can still communicate with each other. National Food Lechon (litson) is an important dish served at many occasions, especially on fiestas. Lechon is a suckling pig, slowly roasted over live coals to make it crispy and tasty. National Footwear Bakya is the national footwear of the Philippines. It was most popular from the 1950s to the 1970s before the introduction of rubber slippers. There are several colors and designs of bakya that suit the taste of most Filipinos. Valuing Our National Symbols Symbols represent a country and its people. We have to respect and value these symbols because they tell something about our country and of who we are as Filipinos. Here are some ways of valuing our national symbols: When singing the national anthem, stand straight and place your right hand on your left chest. Remove your cap or close your umbrella. Ask the people walking to stop while the flag is being raised. Tell other children to stop chatting while singing the national anthem. Most importantly, sing the national anthem wholeheartedly. Retirement of a Flag: A worn-out flag should be disposed of respectfully. It should be burned in a dignified ceremony, not thrown away or used for other purposes. Help in saving and conserving our forests. They serve as habitat of our national bird and other animals. You may also help organizations that promote reforestation, clean and green programs, and tree planting activities. Do not pick flowers when visiting parks. Instead, help in keeping these places clean and beautiful. Avoid throwing thrash in their surroundings. Patronize products that are made here in our country and made by Filipinos. Tell your family and friends to buy products of the Philippines especially those of which are our national symbol. Aside from patronizing our own products, let us use and love our national language. It is good to learn foreign languages, but do not forget to use our own language correctly and proudly.La familia el padre/papa father/dad el hermano brother el hijo son el abuelo grandfather el tío uncle el primo cousin el sobrino nephew el esposo husband el nieto grandson el padrastro stepfather el hermanastro stepbrother la madre/mamá mother/mom la hermana sister la hija daughter la abuela grandmother la tía aunt la prima cousin la sobrina niece la esposa wife la nieta granddaughter la madrastra stepmother la hermanastra stepsister el bisabuelo great-grandfather la bisabuela great-grandmother el tatarabuelo great-great-grandfather la tatarabuela great-great-grandmother el padrino godfather la madrina godmother el ahijado godson la ahijada goddaughter el suegro father-in-law la suegra mother-in-law el cuñado brother-in-law la cuñada sister-in-law el yerno son-in-law la nuera daughter-in-law Mi my mis my nuestro our nuestra our nuestros our nuestras our tu your (informal) tus your (informal) vuestro you all's vuestra you all's vuestros you all's vuestras you all's su (él) his sus (él) his su (ella) her sus (ella) her su (Ud.) your (formal) sus (Ud.) your (formal) su (ellos/ellas) their sus (ellos/ellas) their su (Uds.) you all's (formal) sus (Uds.) you all's (formal) nuestro abuelo our grandfather tu hermano your brother mi casa my house mis casas my houses tus hermanos your brothers sus libros his books Mi, tu, su, nuestro/a/os/as, vuestro/a/os/as must agree with the thing that belongs to you (or me, or him, or her, or them) in number and gender. That means that if the thing that belongs to someone is plural, you must add an "-s" onto the adjective. Nuestro, vuestro must agree in number and in gender with the thing that belongs to us (or to you all). vuestros hijos nuestras hermanas nuestra abuela su hermana his sister mis primos my cousins mis primas my cousins (female) sus padres his parents nuestra hija our daughter tener to have yo tengo I have tú tienes you have él tiene he has ella tiene she has Ud. tiene you (formal singular) have nosotros tenemos we have nosotras tenemos we have vosotros tenéis you all have vosotras tenéis you all have ellos tienen they have ellas tienen they have Uds. tienen you (formal plural) have Nosotros tenemos ocho tíos. We have eight uncles Yo tengo tres hermanos. I have three brothers. Tengo dos hermanas. I have two sisters ¿Cuántos años tienes? How old are you? Tengo dieciocho años. I am 18 years old. Tengo catorce años. I am 14 years old. Yo tengo tres hermanos y una hermana I have three brothers and one sister