A ball of mass $m_1 = 1$ kg strikes a stationary ball of mass $m_2 = 3$ kg with speed $v_1 = 4$ m/s. The collision is perfectly elastic. Find the speeds of both balls after the collision.
For a perfectly elastic collision with a stationary target the speeds after the collision are:
$$v_1' = \frac{m_1 - m_2}{m_1 + m_2} v_1 = \frac{1 - 3}{1 + 3} \cdot 4 = -2 \text{ m/s}$$
$$v_2' = \frac{2 m_1}{m_1 + m_2} v_1 = \frac{2 \cdot 1}{1 + 3} \cdot 4 = 2 \text{ m/s}$$
The minus sign means the first ball bounces back.
$v_1' = -2$ m/s (bounces back), $v_2' = 2$ m/s