The crate has a mass m and rests on the barge which has a mass M and is initially at rest. The coefficient of kinetic friction between the crate and barge is μ. The rope is pulled (or jerked) such that it snaps and as a result the impulse gives the barge a sudden velocity v₀. Determine the time the crate slides on the barge before coming to rest on the barge. Also, what is the final velocity of the barge?