Question

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height \(\frac h3\) while going up and coming down respectively.

• A. \(\frac {\sqrt 2-1}{\sqrt 2+1}\)
• B. \(\frac {\sqrt 3-\sqrt 2}{\sqrt 3+\sqrt 2}\)
• C. \(\frac{\sqrt 3-1}{\sqrt3+1}\)
• D. \(\frac 13\)

Answer 1

The Correct Option is B

Velocity, \(v=\sqrt {2gh}\)

\(\frac h3=\sqrt {2gh}t−\frac 12gt^2\)

\(\frac 12gt^2+\frac h3-\sqrt {2gh}t=0\)

\(\frac {t1}{t2}=\frac {\sqrt {2gh}+\sqrt {gh−2gh/3} }{\sqrt {2gh}−\sqrt {2gh−2gh/3}}\)

\(=\frac {\sqrt 2+\frac {2}{\sqrt 3} }{\sqrt 2−\frac {2}{\sqrt 3}}\)

\(=\frac {\sqrt 3-\sqrt 2}{\sqrt 3+\sqrt 2}\)

So, the correct option is (B): \(\frac {\sqrt 3-\sqrt 2}{\sqrt 3+\sqrt 2}\).