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Answer on Calculus Question for Meli Gomez

Question #3431

The equation for a projectile's height versus time is h(t)=-16t^2+vt+h
A tennis ball machine serves a ball vertically into the air from a height of feet, with an initial speed of 130 feet per second. What is the maximum height,in feet, the ball will attain

Let's take the first derivative:
h'(t) = -32t +v.
The maximum height is obtained when h'(t) = 0:
-32t = -v
t = v/32
t = 130/32 = 4.0625 s

h(4.0625) = -16 (4.0625)2 + 130 *4.0625 +0 = 264.0625 ft.