A projectile has a range of $80 \mathrm{m}$ and reaches a maximum height of $20 \mathrm{m}$. Calculate the angle at which the projectile is fired.

The velocity of a projectile at the initial point $A$ is $\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Its velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) at point $B$ is

Two long parallel plates $A$ and $B$ are separated by a distance of $4 \mathrm{cm}$ with an electric field of $45.5 \mathrm{V} {\mathrm{m}}^{-1}$ between the plates directed normally from plate $A$ to plate $B,$ as shown in the figure. An electron is projected from plate $A$ with velocity $v$ at an angle of $30°$ with the surface of plate $A$. The maximum value of $v$ so that the electron does not hit plate $B$ is
$($Assume gravity free space, charge of electron $=1.6\times {10}^{-19}\mathrm{C}$ and mass of electron $\left.=9.1\times {10}^{-31} \mathrm{kg}\right)$

Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude $v$ each. The separation between the particles at a time when their position vectors (drawn from the point $P)$ are mutually perpendicular, is:

A projectile thrown with an initial velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $\alpha$ with the horizontal, has a range of $5 \mathrm{m}.$ Taking $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and neglecting air resistance, what will be the estimated value of $\alpha ?$