Physics (been trying all day)
posted by bill .
A 62.6 kg astronaut is on a space walk when the tether line to the shuttle breaks. The astronaut is able to throw a 11.0 kg oxygen tank in a direction away from the shuttle with a speed of 13.3 m/s, propelling the astronaut back to the shuttle. Assuming that the astronaut starts from rest,
find the final speed of the astronaut after throwing the tank. Answer in units of m/s.

This is conservation of momentum, first law. There is no net force on the astronaut  bottle system and the initial momentum is zero so:
0 = mass astronaut* velocity astronaut + mass bottle * velocity bottle