Question

Tom throws a ball into the air.

The ball travels on a parabolic path represented by the equation h = -8t 2 + 40t, where h represents the height of the ball above the ground and t represents the time in seconds.
How many seconds does it take the ball to reach its highest point? What ordered pair represents the highest point that the ball reaches as it travels through the air?

Answer 1

h = -8t² + 40t

dh/dt = 0
⇒ d/dt(-8t² + 40t) = 0
⇒ -16t + 40 = 0
⇒ 16t = 40
⇒ t = 40/16 = 2.5s

So it takes 2.5 seconds to reach highest point

h = -8×2.5² + 40×2.5 = -50 + 100 = 50
Ordered pair: (h,t) = (50,2.5)