Question

A spaceship is moving away from Earth at 0.892c when it fires a small rocket in the forward direction at 0.426c relative to the spaceship. Calculate the rocket's speed relative to Earth (in m/s).

Answer 1

Answer:

The rocket's speed relative to Earth is $2.25\times10^{8}\ m/s$.

Explanation:

Given that,

Speed of spaceship = 0.892c

Speed  of rocket = 0.426c

We need to calculate the rocket's speed relative to Earth

Using formula of relative speed

$v=\dfrac{v_{s}-v_{r}}{1-(\dfrac{v_{r}v_{s}}{c^2})}$

Put the value into the formula

$v=\dfrac{0.892c-0.426c}{1-(\dfrac{0.892c\times0.426c}{c^2})}$

$v=c\dfrac{0.892-0.426}{1-0.379992}$

$v=c\times0.7516$

$v=2.25\times10^{8}\ m/s$

Hence, The rocket's speed relative to Earth is $2.25\times10^{8}\ m/s$.