According to the Guinness Book of World Records, the longest home run ever measu

Question

According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy "Dizzy" Carlyle in a minor-league game. The ball traveled 188 m (618 ft ) before landing on the ground outside the ballpark.

A. Assuming that the ball's initial velocity was 45 degress above the horizontal, and ignoring air resistance, what did the initial speed of the ball need to be to produce such a home run if the ball was hit at a point 0.7 m (2.3 ft ) above ground level? Assume that the ground was perfectly flat.

B. How far would the ball be above a fence 2.7 m (8.9 ft ) in height if the fence were 109 m (358 ft ) from home plate?

Explanation / Answer

Let V be the initial speed of the ball. Because the ball was hit angle an angle, there are two speed components: one is in x-direction, and the other one is in the y-direction. The ball travels at a constant speed horizonally but accelerates vertically.

Break down the intial speed

Vx = Vcos45

Vy = Vsin45

find the time it takes the ball to hit the ground 188m away horizonally

x = vt

188 = Vcos45 * t

t = 188 / Vcos45

now equation

Xf = Xi + V*t + 0.5at^2

Xf = final position (0m), Xi = initial position (.7m), a = acceleration, t = time, V = speed in y-direction

we just found the time, which is 188 / Vcos45, plug it in

0 = 0.7 + 0.5*(-9.8)(188 / Vcos45)^2 + Vsin45 * (188 / Vcos45)

=> - 0.7 = - 4.9*(188 / Vcos45)^2 + 188

=> -188.7 = - 4.9*(188 / Vcos45)^2

=> 38.51 = (188 / Vcos45)^2

=> 6.206 = 188 / Vcos45

=> 6.206 * Vcos45 = 188

=> V = 188 / (6.206*cos45)

=> V = 42.84 m/s

The ball was hit with the speed of 42.84 m/s

now Find the it takes the ball to travel 109m

x = vt

109 = 42.84*cos45 * t

t = 3.598 s

Xf = Xi +  V*t + 0.5at^2

Xf = 0.7 + 42.84*sin45*(3.598) + 0.5*(-9.8)*(3.598)^2

Xf = 46.26 m

the ball was 46.26 - 2.7 = 43.56 m above the fence

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