A person weighing 70 kg moving at a speed of 8 m / s catches up and jumps onto a cart weighing 30 kg

A person weighing 70 kg moving at a speed of 8 m / s catches up and jumps onto a cart weighing 30 kg moving at a speed of 2 m / s. To determine their joint speed of movement after that.

According to the law of conservation of momentum, the vector of the momentum of the cart after a person jumps on it will be equal to the vector sum of the impulses of the person and the cart separately. Since the movement of the cart and the person is co-directed:

v (carts with a person) * (m (carts) + m (person)) = v (carts) * m (carts) + v (person) * m (person);

v (carts with a person) = (v (carts) * m (carts) + v (person) * m (person)) / (m (carts) + m (person)) = (30 * 2 + 70 * 8) / (70 + 30) = 6.2 m / s.

Answer: v (carts with a person) = 6.2 m / s.