Question

A rocket ship is 100m in lenght when measure before leaving the launching pad when in flight a ground abserver measure it lenght as 75m. the velocity of rocket ship is

Answer 1

Let $\bf{l_1=100m,l_2=75m}$
use formula,
$\bf{\frac{l_1}{l_2}=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}}$
here, v is the velocity of rocket ship and c is the speed of light in vaccum.

now, 100/75 = 1/√(1 - v²/c²)
4/3 = 1/√(1 - v²/c²)
squaring both sides,
16/9 = 1/(1 - v²/c²)
16(1 - v²/c²) = 9
16 - 16v²/c² = 9
16v²/c² = 7
4v² = 7c²
taking square root both sides,
4v = √7c
v = √7c/4
we know, c = 3 × 10^8 m/s
so, v = 3 × 10^8 × √7/4
v = 1.98 × 10^8 m/s