Vertical projection from ground level

A ball or object is thrown vertically upward from ground level, and the question asks for velocity at a given time, maximum height, time at a certain height, or ratios involving these quantities.

jee-main 2021 Q2 View
A ball is thrown up with a certain velocity so that it reaches a height $h$. Find the ratio of the two different times of the ball reaching $\frac { h } { 3 }$ in both the directions.
(1) $\frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { \sqrt { 3 } - \sqrt { 2 } } { \sqrt { 3 } + \sqrt { 2 } }$
(4) $\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 }$
jee-main 2022 Q2 View
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 $\frac { h } { 3 }$ while going up and coming down respectively.
(1) $\frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 }$
(2) $\frac { \sqrt { 3 } - \sqrt { 2 } } { \sqrt { 3 } + \sqrt { 2 } }$
(3) $\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 }$
(4) $\frac { 1 } { 3 }$