# If a stone is tossed from the top of a 270 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 270, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground?

Jun 28, 2015

Solve $h \left(t\right) = 0$ using the quadratic formula to get:

$t = \frac{10 \pm \sqrt{{10}^{2} - \left(4 \times - 9.8 \times 270\right)}}{2 \times - 9.8}$

$t \cong 4.76$ or $t \cong - 5.78$

Discard the negative solution to get $t \cong 4.76$ seconds.

#### Explanation:

$h \left(t\right)$ is of the form $a {t}^{2} + b t + c$, with $a = - 9.8$, $b = 10$ and $c = 270$

The roots of $h \left(t\right) = 0$ are given by the formula:

$t = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$= \frac{10 \pm \sqrt{{10}^{2} - \left(4 \times - 9.8 \times 270\right)}}{2 \times - 9.8}$

$= - \frac{10 \pm \sqrt{10684}}{19.6}$

$\cong - \frac{10 \pm 103.36}{19.6}$

$t \cong 4.76$ or $t \cong - 5.78$

Discard the negative solution to get $t \cong 4.76$ seconds.

The negative solution relates to a prequel to the story in which the stone is thrown up from the ground $5.78$ seconds before it passes the top of the building on the way back down.