Question

A 87.0 kg astronaut is working on the engines of a spaceship that is drifting through space with a constant velocity. The astronaut turns away to look at Earth and several seconds later is 38.1 m behind the ship, at rest relative to the spaceship. The only way to return to the ship without a thruster is to throw a wrench directly away from the ship. The wrench has a mass of 0.570 kg, and the astronaut throws the wrench with a speed of 22.4 m/s. How long does it take the astronaut to reach the ship?

Answer 1

Answer:

259.62521 seconds

Explanation:

$m_1$ = Mass of astronaut = 87 kg

$m_2$ = Mass of wrench = 0.57 kg

$v_1$ = Velocity of astronaut

$v_2$ = Velocity of wrench = 22.4 m/s

Here, the linear momentum is conserved

$m_1v_1=m_2v_2\\\Rightarrow v_1=\frac{m_2v_2}{m_1}\\\Rightarrow v_1=\frac{0.57\times 22.4}{87}\\\Rightarrow v_1=0.14675\ m/s$

Time = Distance / Speed

$Time=\frac{38.1}{0.14675}=259.62521\ s$

The time taken to reach the ship is 259.62521 seconds