A student with a mass of m1 = 50 kg runs at a speed of v1 = 6 m / s

A student with a mass of m1 = 50 kg runs at a speed of v1 = 6 m / s, having caught up with a cart m2 = 30 kg, moving at a speed of v2 = 2 m / s, jumps up on it. Determine the speed of the student cart.

The impulse of the student p1 = m1 * v1, the impulse of the cart p2 = m2 * v2, the impulse of the cart together with the student p3 = (m1 + m2) v3. According to the law of conservation of momentum, we obtain:
p1 + p2 = p3
m1v1 + m2v2- (m1 + m1) * v3
v3 = m1v1 + m2v2 / m1 + m2 = 50 * 6 + 30 * 2/50 + 30 = 360/80 = 4.5 m / s