$A$ ball is thrown straight upward from the ground with a speed of $20 \,m/s$. The ball is caught on its way down at a point $5 \,m$ above the ground. The time taken by the ball during the entire trip is (assume $g = 10 \,m/s^2$):

$A$ 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........$m$

$A$ diving board is at a height of $h$ from the water surface. $A$ swimmer standing on this board throws a stone vertically upward with a velocity of $16 \,ms^{-1}$. It reaches the water surface in a time of $5 \,s$. In the next $0.2 \,s$, the diver hears the sound from the water surface. What is the speed of sound (in $\,ms^{-1}$)? (Take acceleration due to gravity $g=10 \,ms^{-2}$)

Assertion $(A)$: The displacement of a vertically projected body during the last second of its upward motion is $\frac{g}{2}$.
Reason $(R)$: For a vertically projected body,the acceleration decreases gradually and becomes $\frac{g}{2}$ during the last second of upward motion.

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 of mass $m$ is thrown vertically upwards. Assume the force of air resistance has magnitude proportional to the velocity,and direction opposite to the velocity. At the highest point,the ball's acceleration is