Question

A soccer ball is kicked from the ground at an upwards velocity of 90 feet per second. The equation h(t)=-16t^(2)+90t gives the height of the ball after t seconds. How many seconds will it take for the ball to reach its maximum height?
I need help figuring this out to help my grade

Answer 1

Answer: 2.81 s

Step-by-step explanation:

Given

Ball is kicked upward with velocity $u=90\ ft/s$

Height of the ball is given by the function $h(t)=-16t^2+90t$

Derivative of a function gives the maxima or minima at certain point

$\Rightarrow \dfrac{dh}{dt}=-32t+90\\\\\Rightarrow \dfrac{dh}{dt}=0\\\\\Rightarrow -32t+90=0\\\\\Rightarrow t=\dfrac{90}{32}\\\\\Rightarrow t=2.81\ s$

Thus, it takes ball 2.81 s to reach the top.