A ball is thrown from the top row of seats in a stadium. The function h (t) = - 16t2 + 16t + 96 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?

Question

Mathematics

Matteo Choi

1 June, 04:17

A ball is thrown from the top row of seats in a stadium. The function h (t) = - 16t2 + 16t + 96 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?

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Answers (1)

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Danna Wiggins · Answer 1

3 seconds

Step-by-step explanation:

We assume the ground is where h=0, so the equation we need to solve is ...

0 = - 16t^2 + 16t + 96

Dividing by - 16 gives ...

0 = t^2 - t - 6

Factoring, we get ...

0 = (t - 3) (t + 2)

This has solutions t=3 and t=-2. Since we know the ball won't land 2 seconds before it is thrown, the solution is ...

It will be 3 seconds before the ball hits the ground.