An astronaut of mass 70 kg carries an empty oxygen tank of mass 14 kg. He throws the tank away from himself with a speed of 3 m/s. With what velocity does the astronaut start to move through space?

Answer 1

I guess he and the tank were stationary when this text was written.
Therefore the initial momentum was zero.
Therefore the final momentum is zero, since there are no external forces mentioned.

70 + 14 = 84
initial momentum = 84 * 0 = 0

final momentum = 0 = 70 v + 14 * 3
v = -14 * 3 /70
The - sign means the astronaut moves in the opposite direction from the tank.