Two identical billiard balls are in contact on a smooth table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is:

A particle of mass $m$ strikes elastically with a disc of radius $R$, with a velocity $v$ as shown in the figure. If the mass of the disc is equal to that of the particle and the surface of the contact is smooth, then the velocity of the disc just after the collision is:

A man of mass $60 \mathrm{kg}$ start falling from building of height $80 \mathrm{m}$ with a bag of $2 \mathrm{kg}$ in his hand. After falling through a distance $20 \mathrm{m}$$$, he throw the bag horizontally with respect to him so that he fall in a pond$2\mathrm{m}$ away from the vertical lines of fall. Calculate horizontal distance of bag from the vertical line of fall where it lands.$(\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2})$