An archer stands a distance L away from a target and fires an arrow at the target. The arrow travels at a speed was meas

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An Archer Stands A Distance L Away From A Target And Fires An Arrow At The Target The Arrow Travels At A Speed Was Meas 1 (63.66 KiB) Viewed 33 times

An archer stands a distance L away from a target and fires an arrow at the target. The arrow travels at a speed was measured in the frame of the archer. L S Figure 1: For problem 1. a) (4 points) Let to and t, be coordinates in the frame of the archer. to is the time that the archer releases the arrow and ty is the time that the arrow hits the target. Suppose to = 0. Find t₁. b) (6 points) Now suppose there is a spaceship moving at speed v relative to the archer in the same direction as the arrow (see Fig.1). An observer on this spaceship also sees the archer release the arrow and the arrow hit the tar- get. This observer sees the two events occuring at to and t, respectively. Find to and (hint: do NOT use the time dilation formula. You should directly apply the Lorentz transformation). Write your answer in terms of L, w, v, and c. We're going to go ahead and assume that causality works. In other words, we want causes to precede effects. In this example, you may think of the archer firing the arrow as the cause for the arrow hitting the target. c) (5 points) Now let's consider the speed of the arrow, w. Suppose w = ac where a < 1 and c is the speed of light. Assume that < c. Can causality be violated in the frame of the archer? What about the frame of the spaceship? If your answer is no, show that causality is not violated (in other words, the effect does not happen before the cause). If your answer is yes, give an example of values of a < 1 and v<e where the effect happens before the cause. d) (5 points) This is the same as the previous section, but we're changing one parameter. Suppose w be where b>1 and c is the speed of light. Assume that < c. Can causality be violated in the frame of the archer? What about the frame of the spaceship? If your answer is no, show that causality is not violated (in other words, the effect does not happen before the cause). If your answer is yes, give an example of values of b>1 and v< c where the effect happens before the cause. OK