# An object is thrown vertically from a height of 9 m at  24 m/s. How long will it take for the object to hit the ground?

Jun 2, 2016

I found: $5.2 s$

#### Explanation:

I would suppose that the velocity is in the upwards direction because it is positive and so in:

${y}_{f} - {y}_{i} = {v}_{i} t + \frac{1}{2} a {t}^{2}$
with:
${y}_{f} = 0$ the ground
$a = g$ downwards.

we have:

$0 - 9 = 24 t - \frac{1}{2} \cdot 9.8 {t}^{2}$
$4.9 {t}^{2} - 24 t - 9 = 0$

${t}_{1 , 2} = \frac{24 \pm \sqrt{576 + 176.4}}{9.8} =$
${t}_{1 , 2} = \frac{24 \pm 27.4}{9.8} =$
${t}_{1} = 5.2 s$
${t}_{2} = - 0.3 s$