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

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 70 kg, Jill has a mass of 45 kg, and the crate has mass 15 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 m/s relative to the rate.

a. What is the final speed of the crate if both Jack and Jill jump simultaneously in the same direction?

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

this can be done by the law of conservation of momentum

initial momentum pi = fional momentum pf

pi =pf

0 = (m1*u1)+(m2*u2)

m1 = (70+45) = 115

then 0 = (115*4) + (15*u2)

u2 = -30.66 m/sec

b) after jack jumps

0 = (70*4)+((45+15)*u2)

the crate and jill moves with -4.67 m/sec

Now after jill also jumps off then

(45+15)*4.67 = 15*u3

u3 = 18.68 m/sec

c) if jill jumps first then

0 = (45*4)+((70+15)*u2)

u2 = -2.11 m/sec

now after jack also jumps off

(70+15)*2.11 = 15*u3

u3 = 11.95 m/sec

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