Question

According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy

Answer 1

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-inderect.

The ball travels at a constant speed horizonally but accelerates vertically.

Break down the intial speed
Vx = Vcos59, Vy = Vsin59

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

x = vt
188 = Vcos59 * t
t = 188 / Vcos59

Xf = .5at^2 + Vt + Xi

Xf = final position (0m)
Xi = initial position (.9m)
a = acceleration
t = time
V = speed in y-derection

we just found the time, which is 188 / Vcos59, plug it in

0 = .5(-9.8)(188 / Vcos59)^2 + Vsin59 * (188 / Vcos59) + .9

-.9 = -4.9(188 / Vcos59)^2 + 188*(1.6642)

-313.7845 = -4.9(188 / Vcos59)^2

64.0376 = (188 / Vcos59)^2

8.00235 = 188 / Vcos59

8.00235 * Vcos59 = 188

V = 188 / (8.00235cos59)

V = 45.614 m/s

The ball was hit with the speed of 45.614m/s


Find the it takes the ball to travel 116m
x = vt
116 = 45.614 cos59 * t = 23.4931 * t
t = 4.9376 s

Xf = .5at^2 + Vt + Xi
Xf = .5(-9.8)(4.9376)^2 + 45.614 sin59 (4.9376) + .9
Xf = -119.4617 m + 0.9 m + 193.0543 m

= 74.49267 m.

the ball was 74.49267 - 3 = 71.49267 m above the fence