Question

The distance a freely falling body covers in the nth second is given by S(n)=d(n)-d(n-1). Show s(n) in terms of g, in simplified form.

Answer 1

Explanation:

`s=ut+(1)/(2)gt^2\\if ~the~body~falls~freely,~then~at~t=0,d=0\\s_(n)=d_n=(1)/(2)gn^2\\S_(n-1)=(1)/(2)g(n-1)^2\\distance~covered ~in~nth~second\\S(n)=d(n)-d(n-1)=(1)/(2)gn^2-(1)/(2)g(n-1)^2=\fracg[n^2-(n-1)^2]\\=(1)/(2)g{(n+n-1)(n-n+1)]\\=(1)/(2)g(2n-1)`