Answer:
500 seconds
Explanation:
[tex]m_1[/tex] = Mass of wrench = 2 kg
[tex]m_2[/tex] = Mass of astronaut with spacesuit = 200 kg
[tex]v_1[/tex] = Velocity of wrench = 20 m/s
[tex]v_2[/tex] = Velocity of astronaut with spacesuit
Distance between the astronaut and the ship is 100 m
As linear momentum is conserved
[tex]m_1v_1+m_2v_2=0\\\Rightarrow v_2=\frac{m_1v_1}{m_2}\\\Rightarrow v_2=\frac{2\times 20}{200}\\\Rightarrow v_2=0.2\ m/s[/tex]
Time = Distance / Speed
[tex]Time=\frac{100}{0.2}=500\ s[/tex]
The time it will take the astronaut to coast back to her ship is 500 seconds
