Special Relativity spaceship problem

[Taylor_1989]

1. Homework Statement
You are on earth as a spaceship flies past at a speed of 0.99c relative to the earth. A high-intensity signal light on the ship blinks on and off, each pulse lasting 2.2 × 10^(−6) s, as measured on the spacecraft.

Your laboratory on earth has a length of 56.4m. How long does the spaceship crew measure it to be?

2. Homework Equations
length contraction


3. The Attempt at a Solution
So I am viewing the question like this. If I am standing on the space ship as this is my frame of ref; right? The the proper length would be unknown as proper length is only measure when me for example is at rest, so I the thought that if I am at rest on the ship the earth is moving 0.99c relative to me, therfore I transposed the length contraction formula to get my ans.

L_0= proper length
L= length on earth

so If I use the length contraction formula to solve for L_0 I would get what the i view it on the space ship, is this correct?

my ans was 59.8m from space ship.

Very new to special relatvity so still getting my head round it.

 

[Doc Al]

You have it backwards. The proper length of the lab is the length measured in its rest frame, which is the earth's frame. The spaceship crew will measure that length to be less.