Question

An astronaut in an experimental high speed spacecraft flies a mission several decades in the future. When the astronaut returns from his mission, instruments on board the spacecraft show that the elapsed time of the mission was 17.154 hours. However, in mission control, the elapsed time for the mission was 17.852 hours. How fast was the spacecraft moving?

Answer 1

Answer:

83067919.256 m/s

Explanation:

Time elapsed in according to the clock in the spacecraft = Δt'' = 17.852

Time elapsed in according to mission control = Δt = 17.154

Speed of light = c =3×10⁸ m/s

Time dilation

$\Delta t'=\frac{\Delta t}{{\sqrt{1-\frac{v^2}{c^2}}}}\\\Rightarrow 17.852=\frac{17.154}{{\sqrt{1-\frac{v^2}{c^2}}}}\\\Rightarrow \sqrt{1-\frac{v^2}{c^2}}=\frac{17.154}{17.852}\\\Rightarrow \sqrt{1-\frac{v^2}{c^2}}=0.961\\\Rightarrow 1-\frac{v^2}{c^2}=0.9233\\\Rightarrow \frac{v^2}{c^2}=0.076697\\\Rightarrow \frac{v}{c}=0.2768\\\Rightarrow v=3\times 10^8\times 0.2768=83067919.256\ m/s$

∴ The speed at which the spacecraft was moving is 83067919.256 m/s