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

259.62521 seconds

Step-by-step 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=(m_2v_2)/(m_1)\\\Rightarrow v_1=(0.57* 22.4)/(87)\\\Rightarrow v_1=0.14675\ m/s`

Time = Distance / Speed

`Time=(38.1)/(0.14675)=259.62521\ s`

The time taken to reach the ship is 259.62521 seconds