Question

The function f(t)=−8(t^2)+25 models the height of a ball dropped from 25 feet in the air.

Answer 1

The ball will be fastest right before it hits the ground because of gravity.

First, let's find the value of t where the ball hits the ground.

-8t²+25 = 0

-8t² = -25

t² = $\frac{25}{8}$

t = $\frac{5}{2\sqrt{2}}$

Note: t has to be positive, which is why there is no positive/negative symbol.

Now, let's calculate the derivative of this function. The derivative will give us the speed of the ball for time t.

d/dx = -16t

Now, let's plug in the value of t

-16 ( $\frac{5}{2\sqrt{2}}$ }

= $\frac{-5(8)}{\sqrt{2}}$

= $-20 \sqrt{2}$

Take the absolute value of that because speed can't be negative

$20\sqrt{2}$

That's the speed of the ball. You can convert that into decimal if you'd like.

Have an awesome day! :)