Question

A ball with a mass of `8 kg` moving at `14 m/s` hits a still ball with a mass of `2 kg`. If the first ball stops moving, how fast is the second ball moving?

Answer 1

56m/s.

Explanation:

We need to consider here the conservation of linear momentum. The law of conservation of linear momentum states that the total momentum of an isolated system is conserved, i.e.,
`m_1v_1 + m_2v_2 = m_1v_1^' + m_2v_2^'`
where `m`'s are the masses of the two objects, `v`'s are the magnitudes of velocities before collision and `v^'`'s are the velocities of the objects after collision. We assume that the velocities are non-relativistic so that the masses remain constant.

For a perfectly inelastic collision, as is in the current problem,
`v_2 = 0 & v_1^' = 0`
Therefore, we have, `m_1v_1 = m_2v_2^'`.

Thus, given that `m_1 = 8kg, m_2 = 2kg` and `v_1 = 14m/s`,
`v_2^' = m_1v_1/m_2 = 8**14/2 = 56m/s`.