Two Relativity Problems on relative length

[Kevin Hsu]

Homework Statement

Travelling at 0.8c in your 100m long spaceship you pass a second, identical ship t rest. How long does the second ship appear to you, and how long does our ship appear to it?

Homework Equations

l = (1 - v²/c²)^1/l_o

The Attempt at a Solution

l = (1 - v²/c²)^1/l_o
l = [1 - (0.8c)²/(3.00*10⁸)²]^1/100m
l = 0.36^1/100
l = 1m

I cannot find any mistakes in my calculations, but the answer I calculated differs from the one found in the answer key, 60m. If anyone can please point out the error for me, it'd be greatly appreciated.

Homework Statement

A sphere of diameter 3m travels past the Earth at 1.5*10^8 m/s, what height and width does it have to an observer on earth?

Homework Equations

l = (1 - v²/c²)^1/l_o

The Attempt at a Solution

I plugged into the equation l_o = 3m and v = 1.5*10^8 m/s.
The equation then yielded 0.9m to be the length. Again, it differs from the
answer key, height = 3m and width = 2.6m.

What I don't understand completely is that, does the sphere stretch into an eclipse when it is accelerated to a fraction of the speed of light, so that the height and the width would be different? How then, would one calculate the height and the width separately?


Thanks in advance for any help/pointers!

 

[Simon Bridge]

gamma = 5/3
so, presumably the moving length is 3/5 the rest length ... or 60m.
... when you computed gamma, it looks like you divided by an extra (3x10^8)^2 ... you don't need to do this explicitly because (0.8c)^2/(c)^2 = (0.8)^2.