A  particle of mass  $m$ is projected with velocity $v$ making an angle of $45^o $ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

Derive the formula for time taken to achieve maximum, total time of Flight and maximum height attained by a projectile.

Two bodies are thrown up at angles of $45^o $ and $60^o $, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

The speed of a projectile at its maximum height is $\frac {\sqrt 3}{2}$ times its initial speed. If the range of the projectile is $P$ times the maximum height attained by it, $P$ is equal to

There are two points $P$ and $Q$ on a projectile with velocities $v_P$ and $v_Q$ respectively such that $v_P$ is perpendicular to $v_Q$ and $\alpha$ is the angle that $v_P$ makes with horizontal at point $P$. Find the correct option