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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 In-Class Problems 2 and 3: Projectile Motion Solutions We would like each group to apply the problem solving strategy with the four stages (see below) to answer the following two problems. I. Understand – get a conceptual grasp of the problem II. Devise a Plan - set up a procedure to obtain the desired solution III. Carry our your plan – solve the problem! IV. Look Back – check your solution and method of solution For the first problem we have posed a series of questions for each of the above steps to help you learn how to use the problem solving strategy. We then leave space for your group to answer the question. You don’t need to answer all these questions but they should help you approach the problem. In the second problem, we invite you to try to solve it without help. If you would like some hints, we do pose a series of hints to consider. In-Class Problem 2: Throwing a Stone Down a Hill A person is standing on top of a hill which slopes downwards uniformly at an angle φ with respect to the horizontal. The person throws a stone at an initial angle θ 0 from the horizontal with an initial speed of v 0 . You may neglect air resistance. How far below the top of the hill does the stone strike the ground? 1
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I. Understand – get a conceptual grasp of the problem How would you model the horizontal and vertical motions of the stone? Draw a graph and a coordinate system. Where did you choose your origin? What choices did you make for positive axes? Do your choices for positive directions affect the signs for position, velocity, or acceleration? In terms of your coordinate system, is there any constraint condition for the horizontal and vertical position of the stone when it hits the ground in terms of the specified quantities in the problem (be careful with signs)? Answer: The problem involves constant velocity in the horizontally direction and constant acceleration a in the vertical direction. y I will choose a Cartesian coordinate system with the origin at the point the stone is thrown with vertical upwards positive and horizontal to the right as positive. Therefore a =− g . The key constraint condition is that the point where the stone strikes the hill has y / / y f < 0 and x f > 0 Therefore tan φ = yx f for < 0 or tan = f for > 0 . I f f will choose > 0 . II. Devise a Plan - set up a procedure to obtain the desired solution In terms of your choices that you made in your model, what equations are applicable to this problem? Identify the different symbols that appear in your equation. Are they treated as knowns or unknowns? Do you have enough equations to solve the problem? Identify the quantity that you would like to solve for and design a strategy to find it.
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