Answer
The mass of the second ball is 2.64 m.
Work Step by Step
Let $m_B$ be the mass of the second ball. Let $v_A$ be the initial velocity of the ball of mass $m$. Note that $v_A' = -0.450~v_A$.
We can use conservation of momentum to set up an equation.
$m~v_A + 0 = -0.450~m~v_A + m_B~v_B'$
Since the collision is elastic, we can use Equation 7-7 to set up another equation.
$v_A - 0 = v_B' - v_A'$
$v_A = v_B' + 0.450~v_A $
$v_B' = 0.550~v_A$
We can use this expression for $v_B'$ in the first equation.
$m~v_A + 0 = -0.450~m~v_A + 0.550~m_B~v_A$
$1.450~m = 0.550~m_B$
$m_B = 2.64~m$
The mass of the second ball is 2.64 m.
