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Practice Midterm

Practice Midterm - Solution set for the ph1c practice exam...

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Solution set for the ph1c practice exam November 17, 2007 What’s this? This is the solution set to the practice exam. Instructions Use these solutions as you see fit. 1
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Problem 1 Figure 1: The setup for problem 1 as seen in the bow’s rest frame at t = 0. At t = 0 an arrow is shot at speed 2 v towards a target, initially 1 meter away from the arrow’s tip and moving at velocity v to the right as in Fig(1). Assume v is relativistic. Determine: a: The time it takes in the rest frame (the frame of the bow) for the arrow to pierce the target. b: The speed of the arrow in the target’s frame. c: The time till collision in the target’s frame. d: Distance traveled by the arrow (from release time to collision time) in the target’s frame. e: For extra credit, determine the answers to parts c and d for the arrow’s frame. Solution The solution to this problem is kind of long, implying that I may have made it a little too hard! Part c is the hardest part; it’s ok if you gloss over that. All parts, however, cover some important issues. I suggest everyone get comfortable with Fig(37-8) of Giancoli as well. This is a similar problem, which is more likely to show up on the exam. a: For this part just use the equations for distance. After a time t the position of the arrow is x a = 2 vt while the position of the target is x t = 1 + vt. At collision these two values will be equal. Therefore, 2 v Δ t b = 1 + v Δ t b 2
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giving, Δ t b = 1 v . (1) This part of the problem illustrates an important point. To find the time or length in one frame, special relativity tells you nothing. You need to calculate these values using the material from ph1a. What the equations of special rel-
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