The time of flight of a vertically projected stone is $8 \,s$. The position of the stone after $6 \,s$ from the ground is (Acceleration due to gravity $= 10 \,m/s^2$). (in $\,m$)

$A$ ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).
$(a)$ Plot qualitatively velocity versus time graph.
$(b)$ Plot qualitatively acceleration versus time graph.

Two balls $A$ and $B$ are thrown with the same velocity $u$ from the top of a tower. Ball $A$ is thrown vertically upwards and ball $B$ is thrown vertically downwards. If a ball $C$ is thrown with the same velocity $u$ in the horizontal direction from the top of the tower,and if $t_A = 6 \ s$ and $t_B = 2 \ s$,then the time $t_C$ taken by ball $C$ to reach the ground is equal to........$s$.

$A$ body falling freely under gravity passes two points $30 \ m$ apart in $1 \ s$. From what point above the upper point did it begin to fall? (Take $g = 10 \ m \ s^{-2}$)

$A$ stone thrown down with a speed $u$ takes a time $t_1$ to reach the ground,while another stone thrown upwards from the same point with the same speed takes time $t_2$. The maximum height the second stone reaches from the ground is

$A$ balloon was moving upwards with a uniform velocity of $10 \, m/s$. An object of finite mass is dropped from the balloon when it was at a height of $75 \, m$ from the ground level. The height of the balloon from the ground when the object strikes the ground was around (in $m$). (Take the value of $g$ as $10 \, m/s^2$)