Question

A particle is dropped from the top of a tower, find the ratio of displacements in successive time intervals.​

Answer 1

Answer:

ratio =$\frac{(2n -1)}{(2n +1)}$

Explanation:

displacement in n seconds

Sn = 1/2 gn²

displacement in (n-1) seconds Sn-1= 1/2 g (n-1)²

displacement in (n+1) seconds  Sn+1 = 1/2 g (n+1)²

Sn - Sn-1 = 1/2g [n² - (n-1)²]   . . . . . . .(1)

Sn+1 - Sn = 1/2 g [(n+1)² - n² ]  . . . . . .(2)

$\frac{Sn -(Sn-1)}{(Sn+1) - Sn}$  = $\frac{(n + n-1) (n -n+1)}{(n+1+n) (n+1-n)}$ = $\frac{(2n -1)}{(2n+1)}$