according to Guinness wo Acc ording to Guinness World Records, the longest home
ID: 1784320 • Letter: A
Question
according to Guinness wo Acc ording to Guinness World Records, the longest home run ever mea- sured was hit by Roy "Dizzy" Carlyle in a minor league game. The ball traveled 618 ft before landing on the ground outside the ballpark. (a) If the ball's initial velocity was in a direction 45° above the horizon- tal, 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 3 ft above the ground level? Ignore air resistance, and assume that the ground was perfectly flat. (b) How far would a ball be above a fence 10 ft high if the fence was 380 ft from home plate?Explanation / Answer
We convert all ft data to m (by multiplying by 0,3048).
a)
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-indirect. The ball travels at a constant speed horizontally but accelerates vertically.
Break down the initial 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
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 / Vcos45)^2 + Vsin45 * (188 / Vcos45) + .9
-.9 = -4.9(188 / Vcos45)^2 + 188
-188.9 = -4.9(188 / Vcos45)^2
38.551 = (188 / Vcos45)^2
6.208 = 188 / Vcos45
6.208 * Vcos45 = 188
V = 188 / (6.208cos45)
V = 42.82 m/s
The ball was hit with the speed of 42.82m/s
b)
Find the time it takes the ball to travel 116m
x = vt
116 = 42.82cos45 * t
t = 3.831s
Xf = .5at^2 + Vt + Xi
Xf = .5(-9.8)(3.831)^2 + 42.82sin45 (3.831) + .9
Xf = 45m
the ball was 45 - 3 = 42m above the fence
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