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 the ball's initial velocity was 50 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 0.9 m (3.0 ft) above ground level? Assume that the ground was perfectly flat. Express your answer using two significant figures.

(B)How far would the ball be above a fence 3.0 m (10 ft) high if the fence was 116 m (380 ft) from home plate? Express your answer using two significant figures.

Explanation / Answer

a)

Let intial speed Vx = Vcos50 and Vy = Vsin50

So,
x = vt
188 = Vcos50 * t
t = 188 / Vcos50
Xf = .5at^2 + Vt + Xi
Xf = final position (0m)
Xi = initial position (.9m)
a = acceleration
t = time
V = speed in y-derection
So,
0 = .5(-9.8)(188 / (Vcos50))^2 + Vsin50 * (188 / (Vcos50)) + .9
V = 43.17 m/s or 43 m/s rounded off

b)

The ball was hit with the speed of 43.17m/s
Find the it takes the ball to travel 116m
x = vt
116 = 43.17Cos50 * t
t = 4.18 s
Xf = .5at^2 + Vt + Xi
Xf = .5(-9.8)(4.18)^2 + 43.17sin50(4.18) + .9
Xf = 53.52m
the ball was 53.52 - 3 = 50.52m above the fence
So, 51 m rounded off.

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