Calculating Momentum in Multi-Object Systems

[pokeefer]

Homework Statement

A stationary life raft of mass 160 kg is carrying two survivors with masses of 55 kg and 72 kg, respectively. They dive off the raft at the same instant, the 55 kg person East at 4.4 m/s and the 72 kg person North at 4.2 m/s. At what speed and in what direction does the raft start to move?

Homework Equations

Momentum = mass x velocity
Change in Momentum = change in mass x velocity
Force = Change in momentum / Time

P1 + P2 = P1' + P2'
M1V1 + M2V2 = M1V1' + M2V2'

The Attempt at a Solution

I don't know where to begin.

The law of conservation of momentum has only been applied by me when there has been 2 objects but I never learned how to calculate something such as the raft and two people.

Question worth 6 marks.

 

[willem2]

Momentum is conserved both in the north-south and the east-west direction.

You know all the initial momenta (all of them 0) of the 3 objects, and the final momenta of the two survivors.

 

[pokeefer]

Thanks,

I managed to solve for both speed and direction :)