$A$ man in a balloon rising vertically with an acceleration of $4.9 \, m/s^2$ releases a ball $2 \, s$ after the balloon is let go from the ground. The greatest height above the ground reached by the ball is .......... $m$ :-

$Assertion$ : Two balls of different masses are thrown vertically upward with the same speed. They will pass through their point of projection in the downward direction with the same speed.
$Reason$ : The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

$A$ body is projected vertically upwards. It reaches a point at a height $h$ above the point of projection after some time with a speed of $8 \,m/s$. The maximum height reached by the body is (Acceleration due to gravity $g = 10 \,m/s^2$). (in $m$)

If the water falls from a dam into a turbine wheel $19.6 \ m$ below,then the velocity of water at the turbines is .................. $m/s$ (take $g = 9.8 \ m/s^2$).

$A$ ball is thrown up vertically with a certain velocity so that it reaches a maximum height $h$. Find the ratio of the times at which it is at height $\frac{h}{3}$ while going up and coming down respectively.

$A$ 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 $m$)?