You have been hired to check the technical correctness of an
upcoming sci-fi thriller film. The movie takes place in the space
shuttle. In one scene, an astronaut's safety line is damaged
while she is on a space walk, so she is no longer connected to
the space shuttle. She checks and finds that her thruster pack
has also been damaged and no longer works.
She is 200 m from the shuttle and moving with it (i.e., she is not
moving with respect to the shuttle). She is drifting in space with
only 4 minutes of air remaining. To get back to the shuttle, she
decides to unstrap her 10-kg tool kit and throw it away with all
her strength, so that it has a speed of 8 m/s relative to her. In
the script, she survives, but is this correct? Her mass, including
her space suit, is 80 kg.
m1 * Δv1 = m2 * Δv2 (I think (law of conservation of momentum?))
Time = Distance / Velocity
The Attempt at a Solution
So I did:
80 * x = 10 * 8 (Law of conservation of momentum?)
x= 1 m/s
Time = 200 / 1 = 200 seconds
So she would make it with 40 seconds remaining in air, but this seems way to easy and very very wrong.