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?

The average acceleration vector for a particle having a uniform circular motion over one complete revolution is

$A$ ball is projected from a point with a speed $V_0$ at a certain angle $\theta$ with the horizontal. From the same point and at the same instant,a person starts running with a constant speed $0.5 V_0$ to catch the ball. If the person catches the ball after some time,then the angle of projection of the ball is (in $^{\circ}$)

When a body moves with a constant speed along a circle,

Fill in the blanks given below:
$(a)$ At an angle of .......... the horizontal range of a projectile is maximum.
$(b)$ The angle between the instantaneous velocity and instantaneous acceleration of a particle moving in a circular path with constant speed is ..........
$(c)$ If $\overrightarrow{A} = 4\widehat{i} + 3\widehat{j}$,then $|\overrightarrow{A}| = ..........$

$A$ particle moves in the $XY$-plane with $x$ and $y$ coordinates varying with time $t$ as $x(t) = 5t$ and $y(t) = 5t(27 - t^2)$. At what time $t$ (in seconds) will the direction of velocity and acceleration be perpendicular to each other?