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**1. Homework Statement**

A train moves past a tower at a speed of 0.78c. The train has a rest length of L' = 450m. When the front of the train passes the tower, the clocks in the tower and in the front of the train are synchronized to t=t'=0s. The instant that the back of the train passes the tower, the tower sends a signal which is subsequently detected by the receiver in the front of the train.

a) according to the clock on the train, when is the signal sent?

b) when according to the clock in the tower, is the signal received at the front of the train

c)when according to the clock on the train is the signal received?

d) according to an observer on the tower, how far away is the front of the train when the signal is received?

**2. Homework Equations**

Time dilation equations

Length Contraction

lorentz transformation

**3. The Attempt at a Solution**

for part a, I simply used length/speed which gave me the time.

here I used 450m/0.78c = 1.92x10^-6 s.

The biggest problem I have is part b and c.

I was thinking of applying lorentz transformation:

t=[tex]\gamma[/tex](t'+((vx')/c^2))

where the change in x is the difference between the front of the train to the tower. This should give me the time the signal is sent in the tower's frame.

Also, I applied length contraction to the train to obtain the change in x in the tower's frame. Ultimately though, I don't know how to put all the ideas together.

For part d, I think the only equation that's needed is:

change in x = v * change in t where change in t is the time between signal received and signal sent and x is the distance traveled during time t plus the initial length(after length contraction).

Please help I really want to understand this problem as thoroughly as possible. Thanks!