Question

An 88.0 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 28.2 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. If the wrench has a mass of 0.300 kg, and the astronaut throws the wrench with a speed of 18.0 m/s, how long does it take the astronaut to reach the ship?

Answer 1

Given,

mass of astronaut, m_a = 88 kg

distance from the spaceship, s = 28.2 m

mass of wrench, m_w = 0.3 kg

final velocity of the wrench, u = 18 m/s

final velocity of the astronaut, v = ?

All these values are given relative to the spaceship only

Using conservation of momentum {before throwing, both the astronaut and the wrench are at rest}

m_a*0 + m_w*0 = m_a*v + m_w*u

putting all the values

88*0 + 0.33*0 = 88*v + 0.3*18

v = 0.06136 m/s

Now time taken to travel 28.2 m with this velocity is

t = d/v = 28.2/0.06136

t = 459.582 seconds = 7.66 minutes