A man runs across the roof, top of a tall building and jumps horizontally with the hope of landing on the roof of the next building which is at a lower height than the first. If his speed is 9 m/s. the horizontal) distance between the two buildings is 10 m and the height difference is 9 m, will be able to land on the next building? (Take g = 10 `m//s^(-2)`)

Explanation

Giv en, hrizontal speed of the man `(u_(x))= 9 m//s` Horizontal distance between the two buildings, x =10 m
Height difference between the two buildings, y = y m
and `g = 10 m//s ^(2)`
Let the man jumps from point A and and on the root of the next building at point B.
Taking motion in vertical direction,
`y - ut + 1/2 at ^(2)`
`therefore 9=0 xx t + 1/2 xx 10 xx t ^(2) (because u = u _(v) =0)`
` therefore 9=5t ^(2)`
`t = sqrt ((9)/(5)) = (3)/(sqrt5)`

`= 9 xx (3)/(sqrt5)`
`= (27)/(sqrt5)m ~~12m`
Horizontal distance travelled by the man is greater than 10 m, therefore, he will be able to land on the next building.