Question

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.

Answer 1

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 .............. `