Free-fall and vertical drop

A body is released from rest (or dropped) under gravity, and the question asks for time, distance, velocity, or position at a specific point during the fall.

jee-main 2004 Q3 View
A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $\mathrm { T } / 3$ seconds?
(1) $\mathrm { h } / 9$ metres from the ground
(2) $7 \mathrm {~h} / 9$ metres from the ground
(3) $8 \mathrm {~h} / 9$ metres from the ground
(4) $17 \mathrm {~h} / 18$ metres from the ground.
jee-main 2020 Q21 View
A ball is dropped from the top of a 100 m high tower on a planet. In the last $\frac{1}{2}\,\mathrm{s}$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in $\mathrm{m\,s^{-2}}$) near the surface on that planet is $\underline{\hspace{1cm}}$