Find the time it takes for the ball to return back to ground level? Find the maximum height reached by the ball?

Question

A soccer ball is kicked from 3 feet above the ground. The height, h, in feet of the ball after t seconds is given by the function h=-16t^2+64t+3

Answer 1

Hi Madison,

 

First lets find the maximum height.

 

the height function will follow the path of a parabola  and the vertex of the parabola will be the highest point

 

we can find the t value of the vertex using the formula

 

-b/2a   where a and b are the coefficients of the equation

 

b = 64

a = -16

 

t = -64/2(-16)

t = -64/-32

 

t = 2

 

now evaluate the function at that point to get maximum height

 

-16(2)² + 64(2) + 3 = 67

 

so the maximum height will be 67 ft above the ground

 

now to find the time when it returns to the ground  we need to set the equation to 0  and solve for t

 

-16t² + 64t + 3 = 0

 

use the quadratic formula to solve since we can't factor

 

t = (-b - sqrt(b² -4ac))/2a            ( it is really + or - the SQRT but I couldn't represent that

 

t = (-64 - sqrt(4096 - (-192)))/-32

 

t = (-64 - 65.4828)/-32

 

t = -129.4828/-32

 

t = 4.046338 seconds  ( time when the ball will hit the ground

 

Hope this helps