$A$ ball is projected upwards from the top of a tower with a velocity $50 \, m/s$ making an angle $30^\circ$ with the horizontal. The height of the tower is $70 \, m$. After how many seconds from the instant of throwing will the ball reach the ground? ........ $s$

$A$ 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 $g = 10 \, m/s^2$)

$A$ cannon placed on a cliff at a height of $375 \ m$ fires a cannonball with a velocity of $100 \ ms^{-1}$ at an angle of $30^{\circ}$ above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due to gravity $= 10 \ ms^{-2}$)

An aeroplane moving horizontally with a speed of $720 \, km/h$ drops a food packet while flying at a height of $396.9 \, m$. The time taken by the food packet to reach the ground and its horizontal range are (Take $g = 9.8 \, m/s^2$):

$A$ bowling machine placed at a height $h$ above the earth's surface releases different balls with different angles but with the same velocity $10 \sqrt{3} \text{ m s}^{-1}$. All these balls' landing velocities make angles of $30^{\circ}$ or more with the horizontal. Find the height $h$ (in meters) (acceleration due to gravity $g = 10 \text{ m s}^{-2}$).

$A$ gun can fire shells with maximum speed $v_0$ and the maximum horizontal range that can be achieved is $R = \frac{v_0^2}{g}$. If a target farther away by distance $\Delta x$ (beyond $R$) has to be hit with the same gun,show that it could be achieved by raising the gun to a height at least $h = \Delta x \left[ 1 + \frac{\Delta x}{R} \right]$.