Answer
The change in the ball's momentum is $~~(8.25~kg~m/s)~\hat{j}$
Work Step by Step
We can express the initial velocity in unit-vector notation:
$v_i = (-12.0~m/s)~\hat{j}$
We can express the velocity after impact in unit-vector notation:
$v_f = (3.00~m/s)~\hat{j}$
We can find the change in velocity:
$\Delta v = v_f-v_i$
$\Delta v = (3.00~m/s)~\hat{j}-(-12.0~m/s)~\hat{j}$
$\Delta v = (15.00~m/s)~\hat{j}$
We can find the change in the ball's momentum:
$\Delta p = m~\Delta v$
$\Delta p = (0.550~kg)(15.00~m/s)~\hat{j}$
$\Delta p = (8.25~kg~m/s)~\hat{j}$
The change in the ball's momentum is $~~(8.25~kg~m/s)~\hat{j}$.
