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 diameter of a car wheel is $60 \ cm$. How many radians of angular displacement will the wheel have undergone while the car travels a distance of $1.2 \ km$?

$A$ small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track,the normal reaction is maximum in

Two particles $A$ and $B$ are moving in the $XY$ plane. Particle $A$ moves along a line with equation $y = x$,while particle $B$ moves along the $X$-axis such that their $X$-coordinates are always equal. If particle $B$ moves with a uniform speed of $3 \ m/s$,what is the speed of particle $A$?

$A$ small boy is throwing a ball towards a wall $6 \,m$ in front of him. He releases the ball at a height of $1.4 \,m$ from the ground. The ball bounces from the wall at a height of $3 \,m$,rebounds from the ground and reaches the boy's hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic,how far ahead of the boy did the ball bounce from the ground (in $,m$)?

$A$ person walks in such a way that he covers equal distance in each step. The person takes $2$ steps forward towards East, then takes a right turn and walks $4$ steps towards South, then takes a right turn and walks $6$ steps towards West, and then takes a right turn and walks further. The direction of his final position after a total of $20$ steps walk with respect to his initial position is: