Question

What is ratio of distance moved by freely falling body from rest in 4th and 5th second of journey??

Answer 1

(distance moved in 4th second)/(distance moved in 5th second)

= [x(4) - x(3)] / [x(5) - x(4)] where x(t) = 1/2 gt^2

= 7/9

As a generalization, if an object falls one unit distance in the first unit time, then it will fall 2n-1 units distance in the nth unit time. That is, the ratios of the distances fallen is the sequence of odd numbers:

1:3:5:7:9:11:13:15:17...

(This was the original form in which Galileo discovered the law.)

From which it's very easy to see that the ratio of the fourth to the fifth is 7:9. This is merely a consequence of this formula:

n2=1+3+5+⋯+(2n−1)n terms