Momentum Problem: Jack and Jill on a Crate

[robbondo]

Homework Statement

Jack and Jill are standing on a crate at rest on the frictionless, horizontal surface of a frozen pond. Jack has a mass of m1, Jill has a mass of m2, and the crate has a mass of m. 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 v relative to the crate. What is the the final speed of the crate if jack and jill jump off the crate simoltaneously in the same direction.

Homework Equations

The Attempt at a Solution

I know that this has something to do with momentum

I solved the total momentum of the system equal to zero and solved for the v of the crate Vc.

m1v+m2v+mVc=o and solved for Vc to get

Vc=(m1v+m2v)/(-m)

This is incorrect. I don't really know if I should be using momentum or conservation of energy in this problem. thanks for all your help.

 

[robb_]

which conservation to use? well, when does each apply?

 

[m2003]

Your approach to use momentum is correct. However, you made a mistake in your calculation. The total momentum of the system before the jumps is zero, so the total momentum after the jumps must also be zero. This means that the momentum of Jack and Jill must be equal in magnitude and opposite in direction to the momentum of the crate.

Using this information, we can set up the following equation:

m1v + m2v + mVc = 0

Where v is the speed of Jack and Jill, and Vc is the speed of the crate. Since Jack and Jill are jumping in the same direction, their velocities will add together. This means that the total velocity of Jack and Jill, v, is equal to 2v.

Substituting this into the equation, we get:

m1(2v) + m2(2v) + mVc = 0

Simplifying, we get:

2(m1 + m2)v + mVc = 0

Now, we can solve for Vc by rearranging the equation:

Vc = -2(m1 + m2)v/m

So the final speed of the crate will be equal to -2(m1 + m2)v/m, where v is the speed at which Jack and Jill jump off the crate. This means that the final speed of the crate will be in the opposite direction of Jack and Jill's jump.