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

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 (dh)/(dt)=-32t+90\\\\\Rightarrow (dh)/(dt)=0\\\\\Rightarrow -32t+90=0\\\\\Rightarrow t=(90)/(32)\\\\\Rightarrow t=2.81\ s`

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