A baseball (mass = 140 g) is pitched so that it crosses home plate with a speed of 92.0 mph at an angle of 18.4degree below the horizontal. It is hit directly back up the middle of the field with a speed of 81.0 mph at an angle of 41.3 degree above the horizontal. Find
(a) the impulse delivered to the ball by the bat, and
(b) the magnitude of the average force on the ball, if it was in contact with the ball for 32.0 ms.