A body is dropped from a height h above the ground. Find the ratio of distances fallen in first one second, firt two seconds, first three seconds, also find the ratio of distance fallen in `1^(st)` second, in `2^(nd)` second, in `3^(rd)` second etc.

Explanation

From equation `h=1/2"gt"^(2)[:. h=ut+1/2"gt"^(2)and u =0]`
`h_(1):h_(2) :h_(3) ........=1/2g(1)^(2):1/2g(2)^(2):1/2g(3)^(2):.......`
`=1^(2) :2^(2) :3^(3).......`
`= 1:4:9`
(b) Now from the formula of distance travelled in `n^(th)` second
`s_(n) = u+1/2 a(2n-1) ` where u = 0 , a = g
`:. s_(n) =1/2(2n -1) `
or, `s_(1) : s_(2) : s_(3) .....=1/2 g(2xx1-1) : 1/2 g(2xx2-1)`
`=1/2 g (2xx3xx-1)` .......
`= 1 : 3: 5 ........`