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

$(4t + \sqrt{250})(4t - \sqrt{250}) = 0$

$4t + \sqrt{250} = 0$   or   $4t - \sqrt{250} = 0$

$4t = -\sqrt{250}$   or   $4t = \sqrt{250}$

$t = -\dfrac{\sqrt{250}}{4}$   or   $t = \dfrac{\sqrt{250}}{4}$

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

$t = \dfrac{\sqrt{250}}{4} \approx 4.0$

Answer: 4.0 seconds