A200 kg cart is coasting at a constant velocity of 25 m/s. as the cart coasts 50 kg block is dropped into it. what will be the velocity of the cart now ? m/s

The initial kinetic energy of the cart is

After the block is dropped into the cart, if there are no other forces acting on it, the kinetic energy of the new system cart+block must be conserved, so it should be the same as before. But the new mass will be M+m, where m=50kg is the mass of the block. Therefore we can write

from which we find