Question

The equation h = -16t 2+ 53x + 8 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked. What is the maximum height the football reaches?

Answer 1

Answer: The maximum height the football reaches = 51.89 feet.

Step-by-step explanation:

Given: The equation $h = -16t^2+ 53t + 8$ gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked.

Differentiate the given equation, we get

$h'=-(2)16t+53=-32t+53$   (i)

Put $h'=0$

$\Rightarrow\ -32t+53=0\\\\\Rightarrow\ t=\dfrac{53}{32}\approx1.65625$

Differentiate (i) w.r.t. t, we get

$h''=-32$ < 0  i.e. h is maximum at t= 1.65625

The value of h at t= 1.65625 will be $-16(1.65625)^2+53(1.65625)+8=51.890625\approx51.89\text{ feet}$

Hence, the maximum height the football reaches = 51.89 feet.