Question

Brantley tosses a ball out of a window that is 75 feet in the air. Its initial velocity is 12 feet per second. The path of the ball is represented by h=-16t^2+12t+75. How long does it take for the ball to hit the ground to the nearest hundredth?

Answer 1

`t = 2.57`

Explanation:

Given

`h=-16t^2+12t+75`

Required

Determine the time to hit the ground

The ground is at point 0.

So, to solve this; we simply set
`h =0`, then calculate the value of t

`0=-16t^2+12t+75`

Multiply through by -1

`0=16t^2-12t-75`

Reorder

`16t^2-12t-75 = 0`

Solve using quadratic formula:

`t = (-b\±√(b^2 - 4ac))/(2a)`

Where

`a = 16; b = -12; c = -75`

`t = (-(-12)\±√((-12)^2 - 4*16*(-75)))/(2*16)`

`t = (12\±√(144 +4800))/(32)`

`t = (12\±√(4944))/(32)`

`t = (12\±70.31)/(32)`

Split:

`t = (12+70.31)/(32)` or
`t = (12-70.31)/(32)`

`t = (82.31)/(32)` or
`t = (-58.31)/(32)`

But time (t) can't be negative;

So, we make use of only

`t = (82.31)/(32)`

`t = 2.57`

Hence, the time to hit the ground is 2.57 seconds