Momentum Question

[antiflag403]

Hey everyone!
I am having some trouble with this problem. I would appreciate any help/advice/hints.

A child of mass 33 kg jumps off of a wagon. After jumping, the child's velocity is 4.0 m/s [right]. If the mass of the wagon is 7.2 kg, determine the velocity of the wagon after the child jumps off.

All I have figured is that the childs momentum is 132 Kgm/s right.
I am confused as to how to get the velocity of the wagon now. I do not have enough info to use Momentum= Mass X Velocity.

Any help would be appreciated.

[Christina De Rose]

Just before the child jumps off the wagon, do they have any velocity?

[antiflag403]

I think you mean, is the wagon moving with the child in it?? and if so, i do not know. What i have here is what is given in the question. this is what is messing me up too. im not sure if i should assume the wagons V is 0.

[Integral]

Assume that the wagon is not moving. You know the momentum before (0) and you have the momentum of the child. What must be the momentum of the wagon after the child jumps if momentum is conserved?

[Christina De Rose]

Yeah, well if the wagon just starts moving as the child jumps off, you do:

momentum initial = momentum final
(33kg+7.2Kg)(0) = (33Kg)(4)m/s) + (7.2Kg)(x)

Then, just solve for x

[antiflag403]

the momentum is therefore equal to the momentum of the child????
so......
132=7.2(v)
v= 18.3 m/s
Is that correct??
thanks for the help guys

[juju]

Hi,

If you assume the wagon has a velocioty to start with that is unknown, the proceed like this. (to the right is the positive direction)

The momentum after is M(wagon) *V(wagon after) plus 132.

This is equal to m(wagon plus child)*v(wagon and child before)

You can then solve for V as a function of v.

If v=0, Then V=132/7.2 to the left.

juju

[antiflag403]

ok i'm not sure if i understand. so you are assuming V(Wagon) before is 0 so v=132/7.2. (this is what i was doing) what if you assumed V(wagon) to be 1m/s. can you make an equation for this instance??

[Christina De Rose]

I guess you must assume the initial velocity of the wagon and the child (before he jumps) is zero, unless it is stated in the problem. You can't just asssume the initial velocity is a random number.

[juju]

HI,

The general equation works out to be as follows.

V=(40.2*v-132)/7.2

where V=vleocity of the wagon after the child jumps off

and v=the velocity of the child and the wagon before the child jumps off.

This equation results from equating the total momentum of the wagon and the child before to the total momentum of the wagon and child after.

The velocities are considered positive to the right and negative to the left.

juju