#### Answer

(a) The magnitude of the change in momentum of the ball is $11.31~kg~m/s$
(b) The impulse exerted on the ball by the bat is $11.31~kg~m/s$
(c) The magnitude of the average force exerted on the ball by the bat is $3770~N$

#### Work Step by Step

(a) We can find the change in velocity:
$\Delta v = v_f-v_0 = (-37~m/s)-(41~m/s) = -78~m/s$
We can use the magnitude of the change in velocity to find the magnitude of the change in the ball's momentum:
$\Delta p = m~\Delta v$
$\Delta p = (0.145~kg)(78~m/s)$
$\Delta p = 11.31~kg~m/s$
The magnitude of the change in momentum of the ball is $11.31~kg~m/s$
(b) The impulse exerted on the ball by the bat is equal to the ball's change in momentum, which is $11.31~kg~m/s$
(c) We can use the impulse to find the average force exerted on the ball by the bat:
$F~t = J$
$F = \frac{J}{t}$
$F = \frac{11.31~kg~m/s}{0.0030~s}$
$F = 3770~N$
The magnitude of the average force exerted on the ball by the bat is $3770~N$