A woman and her husband simultaneously dive from a 120 kg raft that is initially
at rest. The woman (60 kg) jumps from the boat with a horizontal speed of 1.9
m/s due south, while her husband (77 kg) jumps with a horizontal speed of 1.5
m/s due west. Calculate the magnitude and direction of the boat’s velocity
immediately after their dives.
The Attempt at a Solution
I calculated the momentum of the woman to be (60)(1.9)=114 kg*m/s south
and the man's momentum to be (77)(1.5)=115.5 kg*m/s west. Since it was at rest, the initial momentum of the boat and the two people would have been zero. I'm confused about how to link the mass of the boat and its velocity to these equations. Will the final momentum of the boat be equal to their two momenta? MbVb=MmanVman+MwomanVwoman? I'm thinking I'll have to use the pythagorean theorem to calculate the direction of the displacement. Any help would be greatly appreciated!