An open topped rail road car of mass M has an initial velocity v0  along a straight horizontal frictionless track. It suddenly starts raising at time t = 0. The rain drops fall vertically with velocity u and add a mass m kg/sec of water. The velocity of car after t second will be (assuming that it is not completely filled with water)

The rain drops falling vertically with velocity u do not affect the momentum along the horizontal track. A vector has no component in a perpendicular direction Rain drops add to the mass of the carMass added in t sec = (mt)kgMomentum is conserved along horizontal track.Initial mass of car = MInitial velocity of car = v0 Final velocity of (car + water) = vMass of (car + water) after time t = (M + m)∴  Final momentum = Initial momentum(M+mt)v=Mv0 ∴v=Mv0(M+mt)