Question

Pekka tosses a ball out of a window that is 40 feet in the air. Its initial velocity is 15

feet per second. The path of the ball is represented by
h = -16t2 + 15t + 40
How long does it take for the ball to hit the ground (in seconds) rounded to the
nearest hundredth?

Answer 1

2.12 seconds

Explanation:

Given

`h(t) = -16t^2 + 15t + 40`

Required

Determine how long the ball hits the ground

When the ball hits the ground means that
`h(t) = 0`

So, we have that:

`h(t) = -16t^2 + 15t + 40` becomes

`0 = -16t^2 + 15t + 40`

Reorder

`-16t^2 + 15t + 40 = 0`

Multiply through by -1

`16t^2 - 15t - 40 = 0`

Solve using quadratic:

`t = (-b\±√(b^2 - 4ac))/(2a)`

Where

`a = 16`
`b = -15`
`c = -40`

So, we have:

`t = (-b\±√(b^2 - 4ac))/(2a)` becomes

`t = (-(-15)\±√((-15)^2 - 4*16*-40))/(2*16)`

`t = (15\±√((-15)^2 - 4*16*-40))/(2*16)`

`t = (15\±√(225 +2560))/(32)`

`t = (15\±√(2785))/(32)`

`t = (15\±52.77)/(32)`

Split:

`t = (15+52.77)/(32)` or
`t = (15-52.77)/(32)`

`t = (67.77)/(32)` or
`t = (-37.77)/(32)`

`t = 2.12` or
`t = -1.18`

But time can't be negative

So:

`t = 2.12`

Hence, time to hit the ground is 2.12 seconds