Question

A man runs across the roof-top of a tall building and jumps horizontally with 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 height difference is ` 9 m`, will he be able to land on the next building ? (take `g=10 m//s^(2)`).

Answer 1

Given, horizontal speed of the man `(u_(x)) = 9 m//s`
Horizontal distance between the two builidings `= 10 m`
Height difference between the two builidings `= 9 m`
and `g = 10 m //s^(2)`
Let the man jumps from point A and land on the roof of the next building at point B.
Taking moton in vertical direction.
`y = ut + 1/2 at^(2)`
`9 = 0 xxt + 1 /2 xx 10 xx t^(2)`
`9 = 5t^(2)`
or `t = sqrt((9)/(5)) = (3)/(sqrt(5))`

`:.` Horizontal distance travelled `= u_(x) xx t = 9 xx (3)/(sqrt(5)) = (27)/(sqrt(5)) m`
`~~ 12 m`
Horizontal distance travelled by the man is greater than `10 m`, therefore, he will land on the next building.