Question

The height, h, in feet of a ball above the ground is given by h = −16t2 + 64t + 80, where t is the time in seconds. How long does it take the ball to hit the ground?

Answer 1

t = 5 seconds

Explanation:

It is given that, the height h, in feet of a ball above the ground is given by :

`h=-16t^2+64t+80`

Where t is in seconds

We need to find how long does it take the ball to hit the ground? When it hits the ground, its height will be equal to 0. So,

`-16t^2+64t+80=0\\\\t=(-64\pm √((64)^2-4* (-16)(80)) )/(2* -16)\\\\t=(-64+ √((64)^2-4* (-16)(80)) )/(2* -16),(-64-√((64)^2-4* (-16)(80)) )/(2* -16)\\\\t=-1\ s\ \text{and}\ t=5\ s`

Neglecting negative time.

It means ball will take 5 seconds to hit the ground.