Question

A 100-kg astronaut is floating in outer space. If the astronaut throws a 2-kilogram wrench at a speed of 10 meters per second, which best describes her velocity?

Answer 1

Since Astronaut and wrench system is isolated in the space and there is no external force on it

So here momentum of the system will remain conserved

so here we can say

$m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$

initially both are at rest

so here plug in all values

$0 = 100 v_{1f} + 2\times 10$

$v_{1f} = -0.20 m/s$

so here the astronaut will move in opposite direction and its speed will be equal to 0.20 m/s