How Does Relativity Affect Perceptions of Time and Length in Motion?

[Oijl]

Homework Statement

A race horse can travel down a 2000m straightaway at a speed of 0.9c.

a) How long does it take the horse to run the straightaway according to a timer sitting in the grandstand?
b) From the jockey's perspective, the length of the straightaway appears to be less than 2000 m. What is the apparent length?
c) How long does it take for the horse to run the straightaway according to the jockey?
d) What would the jockey calculate for the speed of the horse relative to the grandstand?


It seems like I'm doing things right until the last part, but I put up my work for the first three parts so you'll know my thought process that leads me to my problem in part d.

Homework Equations

The Attempt at a Solution

a) ∆t = length/speed
Length of the straightaway according to a timer in the grandstand would be 2000m, because there would be no length contraction for the timer.
length=2000m
The speed is given at 0.9c.
speed=0.9c
Therefore,
∆t = 2000/(0.9c) = some value

b)L = Lo[sqrt(1-(u^2)/(c^2))]
Lo = 2000m
u = 0.9c
So,
L = 2000[sqrt(1-0.9^2)] = some other value

c) Again, ∆t = length/speed (but here we'll call it ∆to)
∆to = L/(0.9c), where L is the L of part b

d) ...
Speed is length over time, and the length according to the jockey is L, and the time according to the jockey is ∆to, which was calculated using 0.9c as the speed, so 0.9c would be the speed of the horse.



Anyway, thanks for looking at this, and I'm sure someone can give me a good, quick help that sets me straight because I know this is a simple problem.

 

[Doc Al]

Looks good to me. The grandstand sees the horse/jockey moving at speed 0.9c, so the horse/jockey sees the grandstand moving at speed 0.9c. (They agree on each other's relative speed.)