An aeroplane flying $490 \, m$ above ground level at $100 \, m/s$ releases a block. How far on the ground will it strike (in $km$)?

$A$ ball of mass $m=1 \, kg$ is thrown from the top of a building with initial velocity $v=(20 \, m/s) \hat{i} + (24 \, m/s) \hat{j}$ at time $t=0$. The change in the potential energy of the ball between $t=0$ and $t=6 \, s$, if the ball does not hit the ground, is (assume $g=10 \, m/s^2$): (in $ \, J$)

$A$ child stands on the edge of a cliff $10 \ m$ above the ground and throws a stone horizontally with an initial speed of $5 \ m/s$. Neglecting air resistance,the speed with which the stone hits the ground will be $.......... \ m/s$ (given,$g = 10 \ m/s^2$).

Two objects are located at a height of $10 \ m$ above the ground. At some point in time, the objects are thrown with an initial velocity of $2 \sqrt{2} \ m \ s^{-1}$ at an angle of $45^{\circ}$ and $135^{\circ}$ with the positive $X$-axis, respectively. Assuming $g = 10 \ m \ s^{-2}$, the velocity vectors will be perpendicular to each other at a time equal to: (in $s$)

Two balls of mass $M$ and $2M$ are thrown horizontally with the same initial velocity $v_{0}$ from the top of a tall tower and experience a drag force of $-kv$ $(k > 0)$,where $v$ is the instantaneous velocity. Then,

$A$ ball is projected from a point $O$ as shown in the figure. It will strike the ground after ........ $s$ $\left(g=10 \, m/s^2\right)$.