$A$ boy throws balls into the air at a regular interval of $2 \, s$. The next ball is thrown when the velocity of the first ball is zero. How high does the ball rise above his hand (in $, m$)? [Take $g = 9.8 \, m/s^2$]

Write the equation for the distance covered by an object falling freely during the $n^{th}$ second.

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.

$A$ boy throws a ball vertically upwards from a bridge with velocity $5 \ m/s$. It strikes the water surface after $2 \ s$. The height of the bridge is (Take $g = 10 \ m/s^2$) (in $m$)

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th} \, s$ after its fall and the next droplet is $34.3 \, m$. At what rate are the droplets coming from the tap? (Take $g = 9.8 \, m/s^2$)

$A$ man drops a ball from the roof of a tower of height $400 \ m$. At the same time,another ball is thrown upwards with a velocity of $50 \ m/s$ from the base of the tower. At what height from the base of the tower will they meet (in $m$)?