Question

How fast would it have to be going past you in order for it to appear only 5.55 m long? Give you answer as a ratio of the velocity to the speed of light c. Consider a 6.05 m long sports car going past you at great speed.

Answer 1

let
Lo = 6.05 m
L = 5.55 m
let v is the speed of the car.

use Lengthcontraction equation,

L = Lo*sqrt(1 - (v/c)^2)

L/Lo = sqrt(1 - (v/c)^2)

(L/Lo)^2 = 1 - (v/c)^2

(v/c)^2 = 1 - (L/Lo)^2

v/c = sqrt(1 - (L/Lo)^2 )

v = c*sqrt(1 - (L/Lo)^2 )

= c*sqrt(1 - (5.55/6.05)^2 )

= 0.398*c

v = 0.398*c (or) v/c = 0.398   <<<<<----Answer