When a pitcher throws a fastball, the $145-g$ baseball goes from rest to a speed of $4\mathrm{.}0{10}^1\frac{m}{s}.$

a$.$ Calculate the work done on the ball by the pitcher.

b$.$ After the windup in the throwing phase of the pitch, the pitcher's arm extends behind the pitcher. At the instant of furthest extension the ball is nearly at rest. The body rotates, the arm moves through an arc, and the ball is released. The time interval of the throwing phase is only about $5\mathrm{.}0{10}^{-2}s.$ Calculate the average power of the pitch during the throwing phase.