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 DizzyCarlyle in a minor league game. The ball traveled 188m (618ft ) before landing on the ground outside the ballpark.

(a) Assuming the ball's initial velocity was 52 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 (3.0 ft) above ground level? Assume that the ground was perfectly flat.

(b) How far would the ball be above a fence 3.0 (10 ft ) high if the fence was 116 m (380 ft) from home plate?

Explanation / Answer

x direction
x = v0x t

188 = v*cos(52 degrees)*t

t = 188/(v*cos(52 degrees))

y direction

y = y0 + v0y t + 1/2 a t^2

0 = 0.9 + v*sin(52 degrees)*t - 0.5*9.81*t^2

0 = 0.9 + v*sin(52 degrees)*(188/(v*cos(52 degrees))) - 0.5*9.81*(188/(v*cos(52 degrees)))^2

solve for v
v=43.5 m/s

b)

x direction

116 = 43.5*cos(52 degrees)*t

t=4.33 s

y direction
y = 0.9 + 43.5*sin(52 degrees)*4.33 - 0.5*9.81*4.33^2 = 57.4 m

so 54.4 m above the fence

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