# Warm-Up Exercise 40

## Due 12:15 pm, Fri 30 Nov 2012

Physics 123, Fall 2012

Reading assignment: 39.6

Look at the velocity transformation equation, Eqn 39.18 (8th edition). In
the context of me throwing a ball forward while riding on a fast train (and
being observed by the class on the ground), u_{x}' = the speed at
which I throw the ball, v = the speed of the train, and u_{x} = the
speed of the ball as measured by the class. Suppose I throw the ball at 0.5
c. What speed does the class observe the ball to travel at when the train is
moving at 0.01 c? 0.50 c? 0.99 c? (Give 4 sig figs.) What do you learn from
those answers?

0.01c --> 0.5075c (compare to 0.51c)
0.50c --> 0.8000c (compare to 1.00c)
0.99c --> 0.9967c (compare to 1.49c)
For situations with small velocities, the answers are close to what Newton would predict. For situations with large velocities, the answer is always limited by the speed of light.

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