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 = Vcos40
Vy = Vsin40

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

x = vt
188 = Vcos40 * t
t = 188 / Vcos40

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 / Vcos45, plug it in

0 = .5(-9.8)(188 / Vcos40)^2 + Vsin45 * (188 / Vcos40) + .9

-.9 = -4.9(188 / Vcos40)^2 + 188

-188.9 = -4.9(188 / Vcos40)^2

38.551 = (188 / Vcos40)^2

6.208 = 188 / Vcos40

6.208 * Vcos40 = 188

V = 188 / (6.208cos40)

V = 39.525 m/s

The ball was hit with the speed of 39.525m/s


Find the it takes the ball to travel 116m
x = vt
116 = 39.525cos40 * t
t = 3.831s

Xf = .5at^2 + Vt + Xi
Xf = .5(-9.8)(3.831)^2 + 39.525sin40 (3.831) + .9
Xf = 26.31m

the ball was 26.31 - 3 = 23.31m above the fence