How long will it take for the astronaut to reach the shuttle?

Question

A 57.7kg astronaut becomes separated from the shuttle, while on a space walk. She finds herself 71.5m away from the shuttle and moving with zero speed relative to the shuttle. She has a 0.983kg camera in her hand and decides to get back to the shuttle by throwing the camera at a speed of 12 m/s in the direction away from the shuttle.
How long will it take for her to reach the shuttle?
Answer in minutes.

Answer 1

This is just conservation of linear momentum. You can solve by determining the momentum of the camera.

p = mv
p = (0.983 kg)(12 m/s)
p = 11.796 kg*m/s

But space is a relatively ideal condition...we know that the astronaut's momentum will be the same as the camera's.

p = mv
11.796 kg*m/s = (57.7 kg)v
v = 0.2044 m/s (approx)

Now you have the speed of the astronaut, you you just need to determine the time it takes him to get back to the shuttle using simply kinematics.

v = d / t

t = d / v

t = (71.5 m) / (0.2044 m/s)

t = 349.7 s

So roughly 5.8 minutes