Special Relativity, Train, Ball

[chandelure]

Homework Statement

A train with proper length L moves at speed 5c/13 with respect to the ground. A ball is thrown from the back of the train to the front. The speed of the ball with respect to the train is c/3. As viewed by someone on the ground, how much time does the ball spend in the air and how far does it travel.

Homework Equations

Lorentz velocity transformation
v(x)= (v(x)'+u)/(1+uv(x)'/c^2)

Length Contraction (?)

The Attempt at a Solution

First I tried to find the speed of the ball with regards to the person on the ground. Using the Lorentz velocity transformation, with v(x)' as c/3 and u as 5c/13, I got v(x)=7c/11
After that I'm not sure about the next step. The answer to the first part of the problem is 11L/3c. However, when I assumed that the ball would need to travel L distance more than the train to get from back to front, I get L/(7c/11-5c/13)=143L/36c. I'm just really confused now. I think I can solve the second part of the question if I figure out what's wrong with my approach to the first.

Thank you!

 

[TSny]

Hello, chandelure. Welcome to PF!

However, when I assumed that the ball would need to travel L distance more than the train to get from back to front, ...

How long is the train according to someone on the ground?

 

[Chestermiller]

As reckoned by observers on the train, how long does it take for the ball to travel from the rear of the train to the front of the train? In the train frame of reference, if the rear of the train is x' = 0 and the ball is thrown at time t' = 0, what are the coordinates x' and t' when the ball arrives at the front of the train? If, in the ground frame of reference, the ball is thrown at x = 0 at time t = 0, what are the ground coordinates x and t when the ball arrives at the front of the train?

Chet