$A$ body is projected horizontally from a height with a speed of $20 \, m/s$. What will be its speed after $5 \, s$ (in $, m/s$)? (Take $g = 10 \, m/s^2$)

$A$ body is projected from the top of a tower with a velocity $\overrightarrow{u} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k} \text{ m/s}$, where $\hat{i}, \hat{j},$ and $\hat{k}$ are unit vectors along east, north, and vertically upwards, respectively. If the height of the tower is $30 \text{ m}$, find the horizontal range of the body on the ground. (Take $g = 10 \text{ m/s}^2$) (in $\text{ m}$)

$A$ ball of mass $0.2 \ kg$ is thrown from a height of $1 \ m$ with an initial velocity of $\sqrt{10} \ m/s$ at an angle of $45^{\circ}$ with the horizontal. Assuming acceleration due to gravity $g = 10 \ m/s^2$, the modulus of the momentum increment during the total time of motion in $kg \cdot m/s$ is:

An aeroplane moving horizontally with a speed of $180\, km/hr$ drops a food packet while flying at a height of $490\, m$. The horizontal range is........$m$.

An aeroplane moving horizontally at a speed of $200 \; m/s$ and at a height of $8 \; km$ is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released? (Take $g = 9.8 \; m/s^2$)

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,