$A$ particle is projected vertically upwards such that it attains a height of $h$ after $5 \ s$ and $9 \ s$ of its motion. The speed of projection is $...... \ m/s$ $(g = 10 \ m/s^2)$.

$A$ stone thrown upward with a speed $u$ from the top of a tower reaches the ground with a velocity $4 u$. The height of the tower is .........

$A$ body is dropped from a tower of height $h$. It reaches the ground at $t = 4\, s$. What is the height of the tower in $m$?

$A$ bead is free to slide down a smooth wire tightly stretched between points $A$ and $B$ on a vertical circle. If the bead starts from rest at $A$,the highest point on the circle,

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.

$A$ body is falling freely from the top of a tower of height $125 \ m$. The distance covered by the body during the last second of its motion is $x \%$ of the height of the tower. Then $x$ is (Acceleration due to gravity $= 10 \ m/s^2$)