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

Explanation

From second equation of motion, i.e h = `(1)/(2) "gt"^(2)" "(h= ut + (1)/(2)"gt"^(2) and u=0)`
`h_1 : h_2 : h_3 ...... = (1)/(2) g(1)^(2) : (1)/(2)g(3)^(2) = 1^(2) : 2^(2) : 3^(2) .......... = 1 : 4 : 9 : ....... . `
Now from th expression of distance travelled in `n^(th)` second `S_n = u + (1)/(2)a (2n-1)`
here `u =0, a= g" "` So `" "S_n= (1)/(2)g(2n-1)` therefore
`S_1 : S_2 : S_3 ......... = (1)/(2) g ( 2xx1- 1) : (1)/(2)g (2xx 2 -1) : (1)/(2)g( 2xx 3 -1)= 1 : 3: 5 .............. `