Question

A 84.5 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 38.9 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 0.613 kg, and the astronaut throws the wrench with a speed of 24.9 m/s. How long does it take the astronaut to reach the ship? Answer in units of s.

Answer 1

Answer:

215.35736 seconds

Explanation:

$m_1$ = Mass of astronaut = 84.5 kg

$m_2$ = Mass of wrench = 0.613 kg

$v_1$ = Velocity of astronaut

$v_2$ = Velocity of wrench = 24.9 m/s

In this system the linear momentum is conserved

$m_1v_1=m_2v_2\\\Rightarrow v_1=\dfrac{m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.613\times 24.9}{84.5}\\\Rightarrow v_1=0.18063\ m/s$

Time is given by

$Time=\dfrac{Distance}{Speed}$

$Time=\dfrac{38.9}{0.18063}=215.35736\ s$

The time it will take the astronaut to get back to the ship is 215.35736 seconds