Question

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?

Answer 1

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

It will go `22.75m` 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=1/2 at^2` where, `h` is the height `a=g` i.e acceleration due to gravity.

Given, `h=60m` and taking `g=9.81 ms^-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 ms^-1`

Then,we find `x=vt=6.5×3.5=22.75m`

Answer 2

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=ut+1/2g t^2`

Inserting given vales we get

`60=0xxt+1/2(9.81) t^2`
`=> t=sqrt((60xx2)/9.81)`
`=> t=3.5\ s`

Distance traveled in `x` direction`=v_ht=6.5xx3.5=22.7\ m`