# Special Relativity: Kinematics

### Problems on time dilation and length contraction

Problem : If observer Bill, who is on a train moving with speed 0.6c , waves to Julie at four second intervals as measured in Bill's frame, how long will Julie measure between waves?

Problem : Bill and Julie are both now on identical trains. Bill's train is moving to the right with velocity (/2)c with respect to Julie's train. Julie measures her train to be 100 meters long. How long does Julie measure Bill's train to be? How long does Bill measure Julie's train to be?

Problem : What must be the average speed of a muon, a certain type of elementary particle, in order for it to travel 20 meters before it decays? The average rest lifetime of a muon is 2.60×10-8 seconds.

Problem : Consider the following scenario: two meter sticks, call the S A and S B are oriented parallel to the y axis, some distance apart. The travel towards one another along the x -direction: that is, S A one moves in the positive x -direction and S B moves in the negative x -direction (see ). S A has paint brushes on its ends, pointing towards S B such that if S B is longer than S A , for example, it will leave paint marks on S B . Show that there is no length contraction in the y -direction (that is, the sticks both appear 1 meter long to each other)? (Hint: assume this is not the case and derive a contradiction).

Figure %: Two y -oriented meter sticks.

Problem : Imagine a train going through a tunnel. The train and the tunnel both have length l in their own frame. The train moves through the tunnel with speed v . There is a bomb at the front of the train which is designed to explode when the front of the train passes out the far end of the tunnel. However, there is a disarming sensor located on the back of the train which will disarm the bomb just as the back of the train enters the near end of the tunnel. Will the bomb explode?

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