# An object is thrown vertically from a height of 2 m at 15m/s. How long will it take for the object to hit the ground?

Sep 8, 2016

Approximately $1.654$ seconds (if I didn't mess up the calculations)

#### Explanation:

For a distance, $d$, an initial velocity, ${v}_{0}$, an acceleration of $a$, and a time of $t$
$\textcolor{w h i t e}{\text{XXX}} d = {v}_{0} t + a {t}^{2}$

In this case
color(white)("XXX")d=-2 " m" (2 meters below the height from with it was thrown)
color(white)("XXX")v_0= 15 " m"/"sec"
$\textcolor{w h i t e}{{\text{XXX")a=-9.8 " m"/(sec}}^{2}}$ (standard gravity assumed)

So we have
#color(white)("XXX")-2.0" m" = 15.0t " m" + (-9.8t^2)" m"

$\textcolor{w h i t e}{\text{XXX}} 98 {t}^{2} - 150 t - 20 = 0$

$\textcolor{w h i t e}{\text{XXX}} t = \frac{150 \pm \sqrt{{150}^{2} - 4 \left(98\right) \left(- 20\right)}}{2 \left(98\right)}$
$\textcolor{w h i t e}{\text{XXX")t=1.65399color(white)("XX}}$ or $\textcolor{w h i t e}{\text{XX}} t = - 0.12386$