A projectile is fired at a speed of $100\, m/sec$ at an angle of $37^o$ above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio $1:3$, the smaller coming to rest. Then the distance of heavier part from the launching point is ........... $m$.

Two particles $A$ and $B$ are projected simultaneously from a fixed point of the ground. Particle $A$ is projected on a smooth horizontal surface with speed $v$, while particle $B$ is projected in air with speed $\frac{2 v}{\sqrt{3}}$. If particle $B$ hits the particle $A$, the angle of projection of $B$ with the vertical is

Two projectiles $A$ and $B$ are thrown with the same speed such that $A$ makes angle $\theta$ with the horizontal and $B$ makes angle $\theta$ with the vertical, then

A stone is projected from the ground with velocity $50 \,m/s$ at an angle of ${30^o}$. It crosses a wall after $3$ sec. How far beyond the wall the stone will strike the ground ..........  $m$ $(g = 10\,m/{\sec ^2})$

A particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to $v$, where

If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile then which of the relation exists?