Jack and Jill are standing on a crate at rest on the frictionless; horizontal surface of a frozen pond. Jack has mass 75.0 kg. Jill has mass 45.0 kg, and the crate has mass 15.0 kg. They remember that they must 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 4.00 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?

Solution 97P Throughout this question, we shall have to consider the momentum conservation principle to answer the questions asked. According to this principle, for a system initial momentum = final momentum. Mass of Jack = 75.0 kg Mass of Jill = 45.0 kg Mass of crate = 15.0 kg (a) When Jack and Jill jump simultaneously, (75.0 + 45.0) kg × 4.0 m/s = (75.0 + 45.0 + 15.0) kg × Speed of crate Speed of crate = 480 kg.m/= 3.56 m/s 135 kg Therefore, the speed of the crate is 3.56 m/s. (b) Jack jumps first, So, 75.0 kg × 4.00 m/s = (75.0 + 45.0 + 15.0) kg × Speed of crate Speed of crate = 3135.0 kgs Speed of crate = 2.22 m/s Jill stays back, So, 45.0 kg × 4.00 m/s = (45.0 + 15.0) kg × Speed of crate Speed of crate = 3.00 m/s Therefore. total speed of the crate = 2.22 m/s + 3.00 m/s = 5.22 m/s (c) Jill jumps first, 45.0 kg × 4.00 m/s = (75.0 + 45.0 + 15.0) kg × Speed of crate Speed of crate = 1.33 m/s Jack stays back, 75.0 kg × 4.00 m/s = (75.0 + 15.0) kg × Speed of crate Speed of crate = 3.33 m/s Therefore, total speed of the crate = 1.33 m/s + 3.33 m/s = 4.66 m/s