# An egg is thrown horizontally off a roof, which is 60 meters high, with an initial velocity of 6.5 m/s. How long does it take to hit the ground, and how far does it go in the x direction?

Aug 11, 2018

It will take $3.5 s$ to reach the ground.

It will go $22.75 m$ in the horizontal direction.

#### Explanation:

The egg will come down because of gravity but due to its imparted horizontal velocity,it will move forward from the bottom of the roof!

So,if it takes time $t$ to reach the ground,considering vertical motion,we can use $h = \frac{1}{2} a {t}^{2}$ where, $h$ is the height $a = g$ i.e acceleration due to gravity.

Given, $h = 60 m$ and taking $g = 9.81 m {s}^{-} 2$ we get,

t=sqrt((2h)/g)=sqrt((2×60)/9.81)=3.5s

So,in this time if it moves a distance of $x$ in the horizontal direction due to constant velocity $v = 6.5 m {s}^{-} 1$

Then,we find x=vt=6.5×3.5=22.75m

Aug 11, 2018

Egg is thrown with horizontal velocity. Therefore, initial vertical velocity of egg $= 0$. Time taken by egg to fall down under gravity and hit the ground can be found by the kinematic expression

$h = u t + \frac{1}{2} g {t}^{2}$

Inserting given vales we get

$60 = 0 \times t + \frac{1}{2} \left(9.81\right) {t}^{2}$
$\implies t = \sqrt{\frac{60 \times 2}{9.81}}$
$\implies t = 3.5 \setminus s$

Distance traveled in $x$ direction$= {v}_{h} t = 6.5 \times 3.5 = 22.7 \setminus m$