A ball having a mass of 0.50 kg and travelling at a speed of 5.0...

According to the law of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision.

$m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f$

Given $m_1 = 0.50 \text{ kg}$, $v_1 = 5.0 \text{ m/s}$, $m_2 = 1.0 \text{ kg}$, and $v_f = 0$.

Substituting the values:

$0.50 \times 5.0 + 1.0 \times v_2 = (0.50 + 1.0) \times 0$

$2.5 + v_2 = 0$

$v_2 = -2.5 \text{ m/s}$

The negative sign indicates that the velocity of the second ball is opposite to the direction of motion of the first ball.