Two objects of equal mass are projected with the same velocity $v$ at the same angle $\theta$ towards each other from a distance $R$. What is the momentum of the system at the moment of collision?

Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$,where $t$ is

$A$ cart moves with a constant speed along a horizontal circular path. From the cart,a particle is thrown up vertically with respect to the cart.

Two projectiles $A$ and $B$ are thrown with the same speed such that $A$ makes an angle $\theta$ with the horizontal and $B$ makes an angle $\theta$ with the vertical. Then:

The second's hand of a watch has $6\, cm$ length. The speed of its tip and the magnitude of the difference in velocities of its tip at any two perpendicular positions will be respectively:

$A$ 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 $(\frac{\pi}{2} - \theta)$ 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