Jack and Jill are standing on a crate at rest on the frictionless, horizontal su

Question

Jack and Jill are standing on a crate at rest on the frictionless, horizontal surface of a frozen pond. Jack has a mass of 75.7kg , Jill has a mass of 44.6kg , and the crate has a mass of 14.1kg . 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 3.60m/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?

Explanation / Answer

a) Conservation of momentum

Initial momentum = 0

Final momentum (75.7+44.6)*v1 + 14.1*v2 = 0

120.3v1 = -14.1v2

v1-v2 = 3.6

120.3(3.6+v2) = -14.1v2

v2 = -3.22 m/s

speed = 3.22 m/s

b) 75.7v1 = -(14.1+44.6)v2

75.7(v2+3.6) = -58.7v2

v2 = -2.027m/s

58.7*-2.027 = 44.6(v3+3.6) + 14.1v3

v3 = -4.762m/s

c) 44.6v1 = -(14.1+75.7)v2

v2 = -1.194m/s

(14.1+75.7)v2 = 75.7(v3+3.6) + 14.1v3

v3 = -4.228m/s

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