# An object is thrown vertically from a height of 6 m at  8 m/s. How long will it take for the object to hit the ground?

Apr 16, 2018

About $2.19$ seconds

#### Explanation:

Find the time it takes to reach the top of the projectile:

$t = \frac{{v}_{f} - {v}_{i}}{g}$

Knowing that at the top of the projectile the velocity is $0 \frac{m}{s}$

$t = \frac{- 8 \frac{m}{s}}{- 9.81 \frac{m}{s} ^ 2} = 0.815 \sec$

Using that time, we can also calculate the distance to the very top:

$v t = d = \left(4 \frac{m}{s}\right) \cdot \left(0.815 s\right) = 3.26 m$

So know we can know that the ball is a total of $6 m + 3.26 = 9.26 m$ off the ground, to calculate the time it takes for the ball to fall downward is:

$t = \sqrt{\frac{2 d}{g}}$

$t = \sqrt{\frac{2 \cdot 9.26 m}{9.81 \frac{m}{s} ^ 2}} = 1.374 s$

To find the total time of the ball in the air, just add the times:
$1.374 s + 0.815 s = 2.19 \sec$