Question 195718
A baseball player has hit a ball. The height, y, of the ball x seconds after it is hit is given by y= -16x^2 + 80x + 3.
At what time will the ball reach its maximum height? I used the quadratic formula and my answer was 2.04
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Find the apogee, which is the vertex of the parabola:
hmax = -b/2a
= -80/(-32) = 2.5 seconds
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What is the maximum height of the ball? I used the original formula.My answer was 232.78
It's at time = 2.5 seconds.
y = -16*2.5^2 + 80*2.5 + 3
ymax = 103 feet
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When will the ball hit the ground? My answer was 4.08
Set y = 0
-16x^2 + 80x + 3 = 0
x = 2.5 + (sqrt(103))/4 seconds
x = ~ 5.037222891 seconds
It's not 5 seconds even, because the ball started up from 3' elevation.