A baseball pitcher pitches a fastball with a horizontal velocity of 40 m/s. The horizontal distance from the point of release to home plate is 17.50 m. The batter decides to seing the bat 0.30 s after the ball was released by the pitcher. The average angular velocity of the bat is 12 rad/s. The angular displacement of the bat from the batter's shoulder to hitting positions above the plate is between 1.5 and 1.8 rad.
a. Will the bat be in a hitting position above the plate when the ball is above the plate? Assumme the pitch is in the strike zone.
b. Assume that the batter does hit the ball. If the bat's instantaneous angular velocity is 30 rad/s at the instant of contant, and the distance from the sweet spot on the bat to the axis of rotation is 1.25 m, what is the instantaneous linear veloity of the sweet spot at the instant of ball contact?