Question

A rocket ship is 200 m long on the ground. when it is in flight it apperars 199 m to an observer on the ground. with what speed is the rocket moving?

Answer 1

Explanation:

A spaceship is 75 m long according to an astronaut on the ship. ... away from Earth, scientists on the ground measure the length of the ship to be 51 m. How fast is the spaceship traveling away from Earth?

Answer 2

The speed of the moving rocket is $\bold{27\times10^6 \ m/s}$

Given:

Length of the rocket ship = 200 m

Length of the rocket ship by the observer = 199 m

To find:

Velocity of the rocket ship = ?

Formula used:

Length contraction is given by the formula:

$\bold{L=L_o\sqrt{1-\frac{v^2}{c^2}}}$

Where,

L = Length seen by the observer (shortened)

$\bold{L_o}$ = Length of the rocket ship

v = Velocity of the rocket ship

c = Velocity of the light in vaccum $\bold{= 3\times10^8 \ m/s}$

Solution:

On substituting the known values in the formula, we get,

$\bold{199=200\sqrt{1-\frac{v^2}{(3\times10^8)^2}}}$

$\bold{\frac{199}{200}=\sqrt{1-\frac{v^2}{9\times 10^{16}}}}$

$\bold{0.995=\sqrt{1-\frac{v^2}{9\times10^{16}}}}$

On squaring both sides, we get,

$\bold{0.99=1-\frac{v^2}{9\times10^{16}}}$

$\bold{\frac{v^2}{9\times10^{16}}=1-0.99}$

$\bold{\frac{v^2}{9\times10^{16}}=0.009}$

On taking square root on both sides, we get,

$\bold{\frac{v}{3\times10^8}=0.09}$

$\bold{v=3\times10^8\times0.09}$

$\bold{\therefore v = 0.27\times10^8 \ m/s=27\times10^6 \ m/s}$