Jack and Jill are standing on a crate at rest on the frictionless horizontal surface of a frozen pond. Jack has mass 74.4 kg, Jill has mass 45.1 kg, and the crate has mass 14.9 kg. They remember that they must go and fetch a pail of water, so each jumps horizontally from the top of the crate. Just after each jumps, that person is moving away from the crate with a speed of 4.40 m/s relative to the crate.
(a) What is the final speed of the crate if both Jack and Jill jump simultaneously and in the same direction? (Hint: Use an inertial coordinate system attached to the ground.)
(b) What is the final speed of the crate if Jack jumps first and then a few seconds later Jill jumps in the same direction?
(c) What is the final speed of the crate if Jill jumps first and then Jack, again in the same direction?