$A$ body freely falling from rest has a velocity $v$ after it falls through a height $h$. The total distance it has to fall down from the starting point for its velocity to become double is: (in $h$)

From a building,two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ is thrown downwards with the same speed $u$ (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground,then:

Two stones are thrown up simultaneously from the edge of a cliff $200 \; m$ high with initial speeds of $15 \; m s^{-1}$ and $30 \; m s^{-1}$. Verify that the graph shown in Figure correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take $g = 10 \; m s^{-2}$. Give the equations for the linear and curved parts of the plot.

Water drops fall from a tap onto the floor,$5 \ m$ below,at regular intervals of time. The first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from the ground at the instant when the first drop strikes the ground is . . . . . . $m$. $(g = 10 \ m/s^2)$

$A$ particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes $t_2$ time to reach the ground from point $B$,then the height of point $B$ from the ground is

$A$ stone is allowed to fall from the top of a tower $100 \ m$ high and at the same time another stone is projected vertically upwards from the ground with a velocity of $25 \ m/s$. The two stones will meet after ......... $s$.