Ted Williams, Professor Emeritus of Hitting with the Boston Red Sox, visits the

Question

Ted Williams, Professor Emeritus of Hitting with the Boston Red Sox, visits the Skydome in Toronto where all distances are measured in meters. He demonstrates to the younger Bluejays how it is done by hitting a home run that clears a low fence 119 m from home plate.

a) What is the minimum speed with which the ball must leave the bat for the batter to have hit a home run? Neglect air resistance (which is actually not completely negligible) and assume the top of the fence is at the same height as the bat.

b) At what angle to the horizontal must the ball leave the bat for this minimum speed to be sufficient? Please enter your answer in degrees.

c) When the ball is hit with the speed and angle determined above, how long does it take the ball to travel the distance to the fence?

d) For these same conditions, find the maximum height (relative to the top of the fence) reached by the ball on its trajectory.

e) Relative to your answer in part (a), what speed would be needed if the ball weighed twice as much? Answer according to the following key:

1 = half as big
2 = 0.707 times as big
3 = the same
4 = twice as big
5 = 1.414 times as big
6 = 4 times as big

Explanation / Answer

let the initial velocity be v at an angle A

So, time taken to reach fence t= 119/(vcosA) [vcosA is the horizontal velocity component]

total change in height of ball=0

so, vsinA t - 0.5 gt2 =0

or, vsinA=0.5gt =0.5g*(119/(vcosA))

or, v2sin2A=0.5*119g

so, for speed to be minimum, sin2A should be maximum i.e =1

so, v =(0.5*119g)

sin2A=1, so A=45 degrees

time taken=119/(vcos45)

The mass of the ball has no effect on its motion.

so, 3=the same

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