What is the force that he exerts ?

Question

As a protest against the umpire's calls, a baseball pitcher throws a ball straight up into the air at a speed of 20.0 m/s. In the process, he moves his hand through a distance of 1.30 m. If the ball has a mass of 0.150 kg, find the force he exerts on the ball to give it this upward speed.

Answer 1

The ball has a weight (weight = mass * gravity) which is directed down toward the ground.
As the pitcher threw the ball straight up they exerted a force on the ball against the force of gravity, thus doing work.

Work = Force * distance

After the work is complete the ball experiences a change in Kinetic energy equal to that of going from rest to 20 m/s. This change in KE equals the magnitude of the work done.
KE = 1/2 mv^2

Calculate the change in KE.
Set the change in KE equal to the work and solve for force.

change in KE = 1/2 (.150 kg) * (20 m/s)^2 = F * (1.30 m)
F = (1/2 (.150 kg) * (20 m/s)^2 ) / (1.30 m) Newtons

Also, this force calculated above is the NET force acting on the ball...not the force the pitcher exerts. Remember that the ball's weight is a force too which is added to the pitcher's force. Since the pitcher's force and the ball's weight act in opposite directions you might call the weight a force which acts in the negative direction and the pitcher's acting on the positive direction.
Keep this in mind when solving for the force which the pitcher exerts on the ball.

Answer 2

The kinetic energy of the ball at the point of release must equal the work done in accelerating it, which is the force times the distance. You want the force, and you have the numbers (mass and velocity) to figure the K.E. The only gotcha is to add the force of gravity to the acelerating force.