Juan hits a baseball. The equation $h = - 16 t^{2} + 120 t$ $h=-16t^2+120t$ models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

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Juan hits a baseball. The equation $h = - 16 t^{2} + 120 t$ $h=-16t^2+120t$ models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

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Answer 1 · 2017-07-15T10:30:24

When the ball returns to ground level, $h = 0$ $h=0$ , so:

$- 16 t^{2} + 120 t = 0$ $-16t^2+120t=0$

This is a quadratic equation we can solve to find the roots $t = 0$ $t=0$ or $t = 7.5$ $t=7.5$ $s$ $s$ , which correspond to the beginning and end of the ball's flight.

Explanation:

For a quadratic in the form $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

We know:

$t = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2} a$ $t=(-b+-sqrt(b^2-4ac))/2a$

For

$- 16 t^{2} + 120 t = 0$ $-16t^2+120t=0$

$a = - 16, b = 120, c = 0$ $a=-16, b=120, c=0$

So:

$t = \frac{- 120 \pm \sqrt{120^{2} - 0}}{- 32} = \frac{- 120 \pm 120}{32} = \frac{0}{- 32} or - \frac{240}{- 32}$ $t=(-120+-sqrt(120^2-0))/-32=(-120+-120)/32=0/-32 or -240/-32$

Therefore:

$t = 0$ $t=0$ or $t = 7.5$ $t=7.5$ $s$ $s$

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Juan hits a baseball. The equation $h = - 16 t^{2} + 120 t$ $h=-16t^2+120t$ models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Juan hits a baseball. The equation h=−16t2+120th=-16t^2+120t models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

1 Answer

Explanation:

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Impact of this question

Juan hits a baseball. The equation $h = - 16 t^{2} + 120 t$ $h=-16t^2+120t$ models the height h, in feet, of the ball after t seconds. How long is the ball in the air?