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 75.8kg , Jill has a mass of 45.0kg , and the crate has a mass of 15.5kg . 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 3.70m/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) AS THEY JUMP TOGETHER

BY MOMENTUM CONSERVATION

(75.8+45)(3.7-V1)=15.5V1

=>V1=3.279 M/S

B)JACK JUMPS FIRST

BY MOMENTUM CONSERVATION

(75.8)(3.7-V1)=(15.5+45)V1

=>2.058 M/S

NOW JILL JUMPS

BY MOMENTUM CONSERVATION

60.5*2.058=15.5V1-45*(3.7-V1)

=>V1=4.81 M/S

C)

JILL JUMPS FIRST

BY MOMENTUM CONSERVATION

(45)(3.7-V1)=(15.5+75.8)V1

=>1.222 M/S

NOW JACK JUMPS

BY MOMENTUM CONSERVATION

91.3*1.222=15.5V1-75.8*(3.7-V1)

=>V1=4.294 M/S

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