# The height h in feet of an object after t seconds is given by the fraction h = -16t^2 + 30t + 8. How long will it take the object to hit the ground? Round answer to the nearest thousandth?

##### 1 Answer
Jun 6, 2017

It will take $2.112$ seconds for object to hit ground.

#### Explanation:

The height of ground level is considered as $0$.

as $h = - 16 {t}^{2} + 30 t + 8$, it will be zero, when

$- 16 {t}^{2} + 30 t + 8 = 0$

or $16 {t}^{2} - 30 t - 8 = 0$ anddividing by $2$

$8 {t}^{2} - 15 t - 4 = 0$

Using quadratic formula $t = \frac{- \left(- 15\right) \pm \sqrt{{\left(- 15\right)}^{2} - 4 \times 8 \times \left(- 4\right)}}{16}$

= $\frac{15 \pm \sqrt{225 + 128}}{16}$

= $\frac{15 \pm \sqrt{353}}{16}$

= $\frac{15 \pm 18.7883}{16}$, but as we cannot have $t$ negative

$t = \frac{33.7883}{16} = 2.112$ seconds