A water balloon is tossed from the top of a walkway so that its height above the ground is found by $h\left(t\right) = −16t^{2} + 20t + 50$ where $h$ is measured in feet and $t$ is measured in seconds.

1. When will the ball reach a maximum height?

   Hint (a):

   The given function is a parabola. Where is the vertex of this parabola?

2. When will the ball hit the ground?

   Hint (b):

   This occurs when $h\left(t\right) = 0$.

3. Approximate the instantaneous velocity of the water balloon when it strikes the ground.

   Step 1(c):

   $\lim \limits_{h\to 0 }\frac{h(2.5+h)-h(2.5)}{h}$

   Step 2(c):

   $\lim \limits_{h\to 0 }\frac{(-16(2.5+h)^2+20(2.5+h)+50)-(-16(2.5)^2+20(2.5)+50)}{h}$