Answer
(a) The velocity of the target ball is 1.7 m/s in the direction that the first ball was moving initially.
(b) The mass of the target ball is 1.2 kg.
Work Step by Step
Let $m_B$ be the mass of the target ball which is initially at rest. Let $v_A$ be the initial velocity of the ball of mass $0.220~kg$.
Since the collision is elastic, we can use Equation 7-7 to set up an equation.
$v_A - 0 = v_B' - v_A'$
$v_B' = 5.5~m/s + (-3.8~m/s)$
$v_B' = 1.7~m/s$
The velocity of the target ball is 1.7 m/s in the direction that the first ball was moving initially.
Now, we use conservation of momentum to set up an equation.:
$m_A~v_A + 0 = m_A~v_A' + m_B~v_B'$
$m_B = \frac{(0.220~kg)(5.5~m/s) - (0.220~kg)(-3.8~m/s)}{1.7~m/s}$
$m_B = 1.2~kg$
The mass of the target ball is 1.2 kg.