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11-31.

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

First determine when the ball hits the ground, or when $h\left(t\right) = 0$.

The ball hits the ground when $t = 2.5$ seconds.

The velocity is the instantaneous rate of change (IROC). See the Math Notes box in Lesson 9.2.1 for the formula.

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

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