$A$ tennis ball is released from a height $h$ and after freely falling on a wooden floor,it rebounds and reaches a height $\frac{h}{2}$. The velocity versus height of the ball during its motion may be represented graphically by (graphs are drawn schematically and not to scale):

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights $a$ and $b$. The ratio of the time taken by the two to cover these distances is

$A$ ball is dropped from the top of a $100\; m$ high tower on a planet. In the last $\frac{1}{2}\; s$ before hitting the ground,it covers a distance of $19\; m$. Acceleration due to gravity (in $m/s^2$) near the surface on that planet is:

$A$ stone is thrown vertically upward with an initial velocity $v_0$. The distance travelled in time $t = \frac{1.5 v_0}{g}$ is

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 falls freely from the top of a tower. It covers $36\%$ of the total height in the last second before striking the ground level. The height of the tower is........$m$