An object thrown vertically upwards reaches a height of 500 m. What was its initial velocity ?
How long will the object take to come back to the earth ? Assume ` g = 10 m//s^(2)`

Explanation

Data `h=500m, g=10m//s^(2).`
`v=0m//s, u=?`, (for the object going up) `+t` (for the object coming down) = ?
As the object moves upward,
`v^(2)+u^(2)+2as`
`=u^(2)+2(-g)h (because a=-g)`
Now, `v=0m//s`
`therefore u^(2)=2gh=2xx10m//s^(2)xx500m`
`therefore u^(2)=(100xx100)m//s^(2)`
`therefore u=100m//s` (initial velocity of the body)
Also, `u=u+at=u-g t`
For v = 0 m/s, u = g t
`therefore 100m//s=10m//s^(2)xxt`
`therefore t` (for the object going up) = 10 s
Now, t (for the object coming down) = t (for the object going up) = 10 s
`therefore " t(for the object going up)" +"t (for the object coming down)"`
`=10s +10s = 20s`
It will take 20 s for the object to come back to the earth.