$A$ projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \; m/s$ and $19.6 \; m/s$ respectively. It will strike the plane after covering a horizontal distance of ........ $m$.

$A$ cannon on a level plane is aimed at an angle $\theta$ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards a vertical cliff a distance $D$ away. Then the height from the bottom at which the shell strikes the side walls of the cliff is

$A$ cricketer can throw a ball to a maximum horizontal distance of $100\, m$. The speed with which he throws the ball is ......... $m/s$ (to the nearest integer).

$A$ ball is projected from the ground into the air. At a height of $5 \text{ m}$, its velocity is $\vec{v} = (5 \hat{i} + 5 \hat{j}) \text{ m s}^{-1}$. The maximum height reached by the ball is (Acceleration due to gravity $g = 10 \text{ m s}^{-2}$): (in $\text{ m}$)

$A$ person can throw a stone to a maximum height of $h$. Determine the maximum horizontal range of the stone in terms of $h$.

The path of a projectile is given by the equation $y = ax - bx^2$, where $a$ and $b$ are constants, and $x$ and $y$ are the horizontal and vertical distances of the projectile from the point of projection, respectively. The maximum height attained by the projectile and the angle of projection are respectively: