Question

A spaceship travels at 0.776c relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to the ship) must it be fired for it to travel at 0.926c relative to Earth?

Answer 1

The velocity of rocket relative to ship is
`2.97*10^(8)\ m/s`

Step-by-step explanation:

Given that,

Velocity of spaceship relative to earth
`v_(se)=0.776c`

Velocity of rocket relative to earth
`v_(re)=0.776c`

We need to calculate the velocity of rocket relative to ship

Using formula of relativistic velocity

`v_(rs)=(v_(re)+v_(es))/(1+(v_(re)v_(es))/(c^2))`

Put the value into the formula

`v_(rs)=(0.776c+0.926c)/(1+(0.776c*0.926c)/(c^2))`

`v_(rs)=c*((0.776+0.926)/(1+0.719))`

`v_(rs)=0.990c`

`v=2.97*10^(8)\ m/s`

Hence, The velocity of rocket relative to ship is
`2.97*10^(8)\ m/s`