Calculate Boat's Velocity After Package Thrown - Boat Linear Momentum Problem

[fishert16]

A child in a boat throws a 6.40kg package out horizontally with a speed of 10m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0kg and the mass of the boat is 45.0kg. Ignore water resistance.

Relevant equations

MV1 + MV2 = M(1+2)V(1+2)

The attempt at a solution

Im not sure what other equations to use. I think possibly [1/2(MVf^2) - 1/2(MVi^2)] + [(MGHf)-(MGHi)] though I am not totaly sure about this.

Could someone lead me in the right direction. I am not sure what goes where.

 

[HallsofIvy]

A child in a boat throws a 6.40kg package out horizontally with a speed of 10m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0kg and the mass of the boat is 45.0kg. Ignore water resistance.

Relevant equations

MV1 + MV2 = M(1+2)V(1+2)

The attempt at a solution

Im not sure what other equations to use. I think possibly [1/2(MVf^2) - 1/2(MVi^2)] + [(MGHf)-(MGHi)] though I am not totaly sure about this.

Could someone lead me in the right direction. I am not sure what goes where.

More correctly M1V1+ M2V= (M1+ M2)(Vi). I presume your M(1+2) is the sum of the two masses- I'm not sure what you meant by "V1+ V2".
Taking the child and boat together to be M1, the package to be M2, M1= 26+ 45= 71 kg and M2= 6.4 kg. What is V2, the velocity of the package, is 10 m/s? You are asked to find V1, the velocity of the child and boat. The only thing you are missing is the inital velocity- and you are TOLD that in the problem. What is it?

 

[fishert16]

So initial velocity is 0 correct? I appreciate this, this is exactly what I needed to know.