Hitting the baseball over the lights Meanwhile at the ballpark Juan was practici

Question

Hitting the baseball over the lights Meanwhile at the ballpark Juan was practicing his hitting while talking to the girls standing around watching. He started telling them how he hit the ball over the 50 foot light tower yesterday. The girls were unsure that he really did that. The formula for this hit is: h(x) = -16x^2 + 60x + 4 where h is the height of the ball and x is the number of seconds the ball is in the air. How can Juan provide proof to the girls that he actually hit the ball over the tower? How high did Juan actually hit the ball? Hitting the ball into the parking lot As Juan continued his hitting practice showing off his abilities, one of the balls flew over the center field stands and into the parking lot. "Did you see that shot", he yelled at the girls. "The ball hung in the air for at least 10 seconds", he exclaimed. The formula for this hit is: h(x) = -16x^2 + 83x + 4 where h is the height of the ball and x is the number of seconds the ball is in the air. How can Juan provide proof that the ball actually hung in the air for 10 seconds? How long did the ball hang actually hang in the air?

Explanation / Answer

h(x) = -16x^2 + 60x +4

A) find the maximum height of ball and check if it is greater than the height of light tower.

x = -b/2a = - (60/2*-16) = 15/8 = 1.875 sec

Max. height : h(1.875) = -16*1.875^2 +60*1.875 +4 = 60.25 ft

He actually hit the ball over the light tower of 50 ft

b) He actually hit the ball over the light tower of 50 ft

He hit 60.25 ft

c) To check how long the ball hung in air, find th time when ball reaches ground

i.e. -16x^2 + 83x + 4 =0

on solving we get x= -0.04 , 5.24

Neglect -ve root

Time ball hung in air = 5.24 sec

d) So, ball hung in air less than 10 sec

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