Question

22 POINTS

The height of a pop fly ball over the time after the ball is hit is modeled by the function, h(t) = -16t2 + 81t + 5, where h is the ball's height in feet above the ground and t is the time in seconds after the ball is hit.

How far above the ground was the ball when it was initially hit?

Answer 1

5 feet

Explanation:

In the height equation (notice the ball's horizontal distance traveled is not addressed here), each term means something.

'5' is where the ball started from, since that makes a difference where it winds up t seconds later. If you have trouble visualizing that, imagine if the ball was batted from the top of a skyscraper. It would take a lot longer to hit the ground than if you hit it from only 5 feet high off the ground!

81t means the ball was hit with enough force to give it an initial upward velocity of 81 feet per unit of t, as it travels forward, so that's 81 feet per second. (Depending on the angle the ball was struck, the horizontal component may be a different number.)

-16t² accounts for Earth gravity pulling the ball downward the whole time, t, the ball is in the air (the negative sign is for downward)

For 22 points, I figured you deserved a very thorough explanation.

Hope this helps!