# An object is thrown vertically from a height of 5 m at  8 ms^-1. How long will it take for the object to hit the ground?

Jan 15, 2016

Assuming the object is thrown downward, the time taken will be $0.48 s$.

#### Explanation:

The question doesn't specify whether the object is thrown upward or downward. I will assume it is thrown downward. This means that the initial velocity, $u = 8 m {s}^{-} 1$, is in the same direction as the acceleration due to gravity, $a = 9.8 m {s}^{-} 2$.

Use the formula $d = u t + \frac{1}{2} a {t}^{2}$, where $d = 5 m$

$5 = 8 t + \frac{1}{2} \cdot 9.8 \cdot {t}^{2} = 8 t + 4.9 {t}^{2}$

Rearranging into standard form for quadratic equations:

$4.9 {t}^{2} + 8 t - 5 = 0$

Use the quadratic formula or your preferred method of solving quadratic equations and take only the positive root:

$t = 0.48 s$

(If the assumption was that the object was thrown upward instead, the initial velocity and the acceleration would have opposite signs: the initial velocity would be $- 8 m {s}^{-} 1$.)