Answer
The speed of the ball just after impact is $~~2.24~m/s$
Work Step by Step
We can find the impulse on the ball:
$J = F~t$
$J = (32~N)(14\times 10^{-3}~s)$
$J = 0.448~N~s$
The impulse on the ball is equal to the change in the ball's momentum.
We can find the speed of the ball just after impact:
$m~v = p$
$v = \frac{p}{m}$
$v = \frac{0.448~N~s}{0.20~kg}$
$v = 2.24~m/s$
The speed of the ball just after impact is $~~2.24~m/s$