A 75 kg swimmer dives horizontally off a 500 kg raft. If the diver's speed immediately after leaving the raft is 4 m/s, what is the corresponding raft speed?
Right Ans: 0.6 m/s
1 Answer

This is about conservation of momentum. For the moment lets assume that the all velocities are in the reference frame of the raft (otherwise there are too many variables in the equation to solve.)
We're given:
mass swimmer = 75kg
mass raft = 500kg
divers speed after = 4m/s
we want:
raft speed after = x
mass(swimmer before)*velocity(swimmer before) + mass(raft before)*velocity(raft before) = mass(swimmer after)*velocity(swimmer after) + mass(raft after)*velocity(raft after)
75kg*0m/s + 500kg*0m/s=75kg*4m/s +500kg* x m/s
0=300kgm/s + 500kg* x m/s
300kg m/s = 500kg* x m/s
.6 m/s = raft velocity