Question

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

a.1000s
b. 500s
c. 250s
d.125s
e. none of these

Answer 1

500 seconds

Step-by-step explanation:

`m_1` = Mass of wrench = 2 kg

`m_2` = Mass of astronaut with spacesuit = 200 kg

`v_1` = Velocity of wrench = 20 m/s

`v_2` = Velocity of astronaut with spacesuit

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`

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