# Homework Help: Relativity - Length Contraction Problem

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1. Jan 8, 2016

### Jacob Ward

1. The problem statement, all variables and given/known data
You are watching a race between two space ships who pass you moving at different constant speeds. In your reference frame, both ships are the same length while moving. It takes the first ship 26.8 minutes to get to the finish line a distance 14 light-minutes away. It takes the second ship 28.2 minutes to travel the same distance. What is the ratio of the length of the first ship to that of the second ship when they are both at rest?

2. Relevant equations
L' = L*Sqrt(1-v^2/c^2)

3. The attempt at a solution
TimeShip1 = 26.8 (*in minutes*);
TimeShip2 = 28.3 (*in minutes*);
DistanceOfRace = 14 (*in light-minutes*);
VelocityShip1 = DistanceOfRace/TimeShip1;
VelocityShip2 = DistanceOfRace/TimeShip2;
LengthShip1 = ???
LengthShip2 = ???

L'=LengthShip1*Sqrt[1 - (DistanceOfRace/TimeShip1)^2] =
LengthShip2*Sqrt[1 - (DistanceOfRace/TimeShip2)^2]

LengthShip1/LengthShip2 = (1/Sqrt[1 - (DistanceOfRace/TimeShip1)^2])/(1/
Sqrt[1 - (DistanceOfRace/TimeShip2)^2]);

I get an answer of 1.01918 but my teacher says the answer is 0.9823 which is exactly the inverse.
This doesn't make sense to me conceptually because if the first ship is going faster (less time to complete the race) it's length should be contracted more which means it is naturally longer than ship 2 and therefore the ratio of ship 1 to ship 2 should be greater than 1 right? which would support my answer.

2. Jan 8, 2016

### TSny

I agree that the ratio should be greater than 1 and I agree with your reasoning. (I haven't check the numerical answer.)