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

The rocket's speed relative to Earth is
`2.25*10^(8)\ m/s`.

Step-by-step 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=(v_(s)-v_(r))/(1-((v_(r)v_(s))/(c^2)))`

Put the value into the formula

`v=(0.892c-0.426c)/(1-((0.892c*0.426c)/(c^2)))`

`v=c(0.892-0.426)/(1-0.379992)`

`v=c*0.7516`

`v=2.25*10^(8)\ m/s`

Hence, The rocket's speed relative to Earth is
`2.25*10^(8)\ m/s`.