$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).

$A$ body is thrown vertically upwards. At half of the maximum height,its velocity is $10 \ m/s$. What is the maximum height attained by the body? (Take $g = 10 \ m/s^2$)

$A$ boy is standing on top of a tower of height $85 \, m$ and throws a ball in the vertically upward direction with a certain speed. If $5.25 \, s$ later he hears the ball hitting the ground,then the speed with which the boy threw the ball is .......... $m/s$ (take $g = 10 \, m/s^2$ and speed of sound in air $= 340 \, m/s$).

$A$ body is falling freely from a point $A$ at a certain height from the ground and passes through points $B, C$,and $D$ (vertically as shown below) such that $BC = CD$. The time taken by the particle to move from $B$ to $C$ is $2 \ s$ and from $C$ to $D$ is $1 \ s$. The time taken to move from $A$ to $B$ in seconds is

If a particle takes $t$ seconds less and acquires a velocity of $v \ ms^{-1}$ more in falling through the same distance (starting from rest) on two planets where the accelerations due to gravity are $2g$ and $8g$ respectively,then $v=$

$A$ ball is dropped from a high-rise platform at $t=0$ starting from rest. After $6$ seconds,another ball is thrown downwards from the same platform with a speed $v$. The two balls meet at $t=18\,s$. What is the value of $v$ in $m/s$? (Take $g= 10\,m/s^2$)