Answer:
The rocket's speed relative to Earth is [tex]2.25\times10^{8}\ m/s[/tex].
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
[tex]v=\dfrac{v_{s}-v_{r}}{1-(\dfrac{v_{r}v_{s}}{c^2})}[/tex]
Put the value into the formula
[tex]v=\dfrac{0.892c-0.426c}{1-(\dfrac{0.892c\times0.426c}{c^2})}[/tex]
[tex]v=c\dfrac{0.892-0.426}{1-0.379992}[/tex]
[tex]v=c\times0.7516[/tex]
[tex]v=2.25\times10^{8}\ m/s[/tex]
Hence, The rocket's speed relative to Earth is [tex]2.25\times10^{8}\ m/s[/tex].
