A baseball pitcher pitches a fastball with a horizontal velocity of 40 m/s. The

Question

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 17.5 m. The batter decides to swing the bat .30s after the ball has been 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? Assume the pitch is in the strike zone.

b.)Assume that the batter does hit the ball. If the bat's instantaneous linear velocity of the sweet spot at the instant of ball contact?

Explanation / Answer

time taken for ball to reach t1=17.5/40=0.437s

Time for strike t2=t1-0.3=0.137s

Angle=angulae velocity*t2=1.64 rad

As 1.64 lies in the range 1.5 to 1.8 rad

Hence,yes the bat will be in a hitting position

B) linear velocity is V=r*W=12*17.5=210 m/s

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