Length contraction equation help

[Ashley1nOnly]

Homework Statement

After year of over-eating and no exercise, Uncle Joe's is overweight, with a waist 50cm wide. He's also out of shape and can only hold his breath for 20 seconds. Worse, he can only jump 20cm high. But at his high-school reunion, he'd like to fool his old friends who haven;t seen him in years, into thinking otherwise by using special relativity. If he speeds by them on a vehicle that's traveling horizontally at (3/5)c, and he's standing vertically, holding his breath, and then jumping vertically, what will they observe for Uncle Joe's waist size (width), breath-holding time, and jumping height.

Homework Equations

L=L0 Sqrt(1-(v/c)^2)

The Attempt at a Solution

where v=3/5c c= 3.0*10^8 and L0= 50

I want to know if this is the right equation and if I am using it right

 

[Simon Bridge]

Depends on your reasoning ... that is certainly the length contraction equation: $L = L_0/\gamma$ this means that $L<L_0$ - is that what you want?

note: $v \neq 3/5c$ you are told that $v=(3/5)c = 3c/5$ (pedantic I know, but pedantery is important in relativity)
... this means that $(v/c)=3/5 \implies (v/c)^2 = 9/25$, so now you don't need a value for $c$ for your equation... in fact the numbers have been chosen so you don't need a calculator.
Also - what about how long he can hold his breath for?