$A$ stone is dropped into water from a bridge $44.1 \ m$ above the water. Another stone is thrown vertically downward $1 \ s$ later. Both strike the water simultaneously. What was the initial speed of the second stone in $m/s$?

$A$ ball is projected vertically upwards from the ground. It reaches a height $h$ in time $t_1$,continues its motion,and then takes a time $t_2$ to reach the ground. The height $h$ in terms of $g, t_1$,and $t_2$ is ($g =$ acceleration due to gravity).

$A$ ball is thrown vertically upwards with a velocity of $15 \ m/s$. To what maximum height will it reach? (Take $g = 10 \ m/s^2$)

When a ruler falls vertically, $5$ different persons catch it with different reaction times. $(g = 9.8 \text{ ms}^{-2})$
$A$. Person $A$ has reaction time of $0.20 \text{ s}$
$B$. Person $B$ has reaction time of $0.22 \text{ s}$
$C$. Person $C$ has reaction time of $0.18 \text{ s}$
$D$. Person $D$ has reaction time of $0.19 \text{ s}$
$E$. Person $E$ has reaction time of $0.21 \text{ s}$
What is the correct order of the distance travelled by the ruler for each person?

Consider a rubber ball freely falling from a height $h = 4.9 \ m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be represented by which of the following graphs?

$A, B, C$ are points in a vertical line such that $AB = BC$. If a body falls freely from rest at $A$, and $t_1$ and $t_2$ are the times taken to travel distances $AB$ and $BC$ respectively, then the ratio $(t_2 / t_1)$ is: