Physics: Aspaceship 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?

What exactly has to be in the presentation ???...

Aspaceship travels at 0.776c relative to earth.

daonewest09

31.12.2021

The velocity of rocket relative to ship is $2.97\times10^{8}\ m/s$

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

$v_{rs}=\dfrac{v_{re}+v_{es}}{1+\dfrac{v_{re}v_{es}}{c^2}}$

Put the value into the formula

$v_{rs}=\dfrac{0.776c+0.926c}{1+\dfrac{0.776c\times0.926c}{c^2}}$

$v_{rs}=c\times(\dfrac{0.776+0.926}{1+0.719})$

$v_{rs}=0.990c$

$v=2.97\times10^{8}\ m/s$

Hence, The velocity of rocket relative to ship is $2.97\times10^{8}\ m/s$

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