Two particles $A$ and $B$ are moving in horizontal plane as shown in figure at $t = 0$ , then time after which $A$ will catch $B$ will be.......$s$

A stone projected with a velocity u at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity u at an angle $\left( {\frac{\pi }{2} - \theta } \right)$ with the horizontal, it reaches maximum height $ H_2$. The relation between the horizontal range R of the projectile, $H_1$ and $H_2$ is

A projectile is fired with a speed $u$ at an angle $\theta$ with the horizontal. Its speed when its direction of motion makes an angle ‘$\alpha $’ with the horizontal is

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

An object is thrown along a direction inclined at an angle of ${45^o}$ with the horizontal direction. The horizontal range of the particle is equal to

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