Question

How long will it take the ball to reach the ground

Answer 1

When the ball reaches the ground, its height is 0.
We set the height function equal to zero and solve for t, the time.

h = -16t^2 + 250

-16t^2 + 250 = 0

16t^2 - 250 = 0


`(4t + √(250))(4t - √(250)) = 0`


`4t + √(250) = 0` or
`4t - √(250) = 0`


`4t = -√(250)` or
`4t = √(250)`


`t = -(√(250))/(4)` or
`t = (√(250))/(4)`

We discard the negative solution since time must be positive.
The positive solution is


`t = (√(250))/(4) \approx 4.0`

Answer: 4.0 seconds