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 74.2kg , Jill has a mass of 44.1kg , and the crate has a mass of 15.8kg . 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)

here , Using conservation of momentum

v*(15.8 )- (74.2 + 44.1)*3.60 = 0

v = 27 m/s

the speed of crate is 27 m/s

b)

Now , when jack jumps ,

v1 (15.8 + 44.1) - 74.2 * 3.6 = 0

v1 = 4.46 m/s

Now , When jill jumps

15.8 * v2 + 44.1 * (4.46 - 3.6) = (15.8 + 44.1)*4.46

solving for v2

v2 = 14.51 m/s

the speed of crate is 14.51 m/s

c)

For jill jumping first

v1 * (74.2 + 15.8) - 44.1 * 3.6 = 0

v1 = 1.764 m/s

Now , when jack jumps

15.8 * v + 74.2 (1.764 - 3.6) = (74.2 + 15.8)*1.764

V =18.7 m/s

the speed of crate is 18.7 m/s

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