Suppose that two small spacecraft, each with a mass of 2000 kg, are drifting next to each other. One of them has an astronaut on board; with her equipment, she has a mass of 200 kg. Both craft are moving in the x−direction at a velocity of ⃗vi = (0.5 m/s, 0). An astronaut wants to travel from one to the other. She pushes off of one spacecraft and jumps onto the other craft; as she floats through the air, she travels in the y−direction with a velocity of ⃗va = (0, 1 m/s). Note that when she moves through the air, she is moving only in the y-direction.
(a) What will the velocity of the first spacecraft be after she jumps off of it? (Velocity is a vector; you can give its components.)
(b) What will the velocity of the second spacecraft be after she lands on it?
(c) Explain in words why the y−components of their final velocities are almost equal and opposite, but are not quite the same magnitude.
(d) Explain in words why the x−components of their final velocities are almost equal.