You are watching a baseball game on tv and a player hits a ball but before you c

Question

You are watching a baseball game on tv and a player hits a ball but before you could see the outcome, the tv is shut off. You are given the facts about the hit, the ball was going to travel 300 ft, it would reach a maximum of 50 ft, and it would take 4 seconds to travel its complete distance. You also know that the height of the outfield fence is 15 ft and the fence is 275 ft away from where the baseball player hit the ball. Did the player hit the baseball over the fence? Show work to prove why or why not.

Explanation / Answer

the ball should travel a horizontal distance of 275ft and a vertical distance of minimum 15ft to clear the fence.

First we find the u, from the given data

the ball was going to travel 300 ft

means R = 300 ft

u^2sin2/g = 300 -----------------------1

maximum of 50 ft

maximum height H = u^2sin^2()/2g = 50 ------------2

dividing 1 and 2 we get

4cot = 6

= 33.69 degrees

from eqn 1

u^2 = 300*32.15/(sin2*33.69) = 10448.76

u = 102.22 ft/s

once you got these results all that is left is to check the height when it is at 275ft away

275 = 102.22*cos(33.69)*t

t = 3.233 sec

vertical distance after t = 3.233 sec is

102.22*sin33.69)*3.233-1/2*32.15*(3.233)^2

= 15.30 ft

yes it barely clears the field and goes out of the fence

for any doubts contact

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