A 26 kg child is coasting at 2.0 m/s over flat ground in a 5.0 kg wagon. The child drops a 1.5 kg ball from the side of the wagon. What is the final speed (in m/s) of the child and wagon

Final speed = 2.067 m/s

Explanation:

We are told that the child weighs 26 kg.

Also, that the wagon weighs 5kg.

Thus, initial mass of the child and wagon with ball is;

m_i = 26 + 5 = 31 kg.

Also, we are told that the child now dropped 1.5 kg ball from the wagon. So,

Final mass is;

m_f = 26 + 5 - 1 = 30 kg

Now, from conservation of linear momentum, we know that;

Initial momentum = final momentum

Thus;

m_i * v_i = m_f * v_f

Where v_i is initial velocity and v_f is final velocity.

Making v_f the subject, we have;

v_f = (m_i * v_i) / m_f

We are given that initial velocity v_i = 2 m/s

Plugging in the relevant values, we have;

v_f = (31 * 2) / 30

v_f = 2.067 m/s