Question

Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long does it take her to coast back to her spaceship

Answer 1

The time it will take the astronaut to coast back to her ship is 500 seconds

Step-by-step explanation:

Mass of wrench, m₁ = 2 kg

Mass of astronaut with spacesuit, m₂ = 200 kg

Velocity of wrench, v₁ = 20 m/s

Velocity of astronaut with spacesuit v₂

Distance between the astronaut and the ship is 100 m

As linear momentum is conserved

`m_1v_1+m_2v_2=0\\\\\Rightarrow v_2=(m_1v_1)/(m_2)\\\\\Rightarrow v_2=(2* 20)/(200)\\\\\Rightarrow v_2=0.2\ m/s`

`Time = ( Distance)/(Speed)`

`Time=(100)/(0.2)=500\ s`

Hence, The time it will take the astronaut to coast back to her ship is 500 seconds