Define projectile motion and projectile particle.

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1}, {R}_{2}$ and ${H}_{1}$, ${H}_{2}$ respectively. Choose the correct option:

A particle is projected from the ground at an angle of $\theta $ with the horizontal with an initial speed of $u$. Time after which velocity vector of the projectile is perpendicular to the initial velocity is

If a body $A$ of mass $M$ is thrown with velocity $v$ at an angle of ${30^o}$ to the horizontal and another body $B$ of the same mass is thrown with the same speed at an angle of ${60^o}$ to the horizontal. The ratio of horizontal range of $A$ to $B$ will be

The equation of a projectile is $y =\sqrt{3} x -\frac{ gx ^2}{2}$ the angle of projection is

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