Question

An object is dropped from a certain point $A$ at a height 'h' from the ground. During its journey straight downwards, the object passes points $B$ and $C$ such that the ratio of time taken $t_1$ to cover $A B$ and $t_2$ to cover $B C$ is $1 : (\sqrt{2}-1)$. What is the ratio of distances $A B : B C$?

• A. $\sqrt{2} : 1$
• B. $(\sqrt{2}-1) : 1$
• C. $1 : 1$
• D. $1 : \sqrt{2}$

Hint:

For any object dropping from rest, the times taken to cover consecutive equal distances are always in the specific ratio: $1 : (\sqrt{2}-1) : (\sqrt{3}-\sqrt{2}) : \dots$ Since the provided times match this exact pattern, the distances must be equal!

Answer 1

The Correct Option is C