Two balls of equal masses are thrown upwards along the same vertical direction at an interval of $2 \mathrm{s}$, with the same initial velocity of $39.2 \mathrm{m} {\mathrm{s}}^{-1}$. The two balls will collide at a height of

A block of mass $2 \mathrm{kg}$ collides with identical stationary block head on elastically with velocity of $20 \mathrm{m} {\mathrm{s}}^{-1}$. After collision second block collides with the third block of mass $2 \mathrm{kg}$ initially at rest. If they collide head on perfectly inelastically then the velocity of their combination will be

A block of mass $m$ rests on a rough horizontal surface (Coefficient of friction is $\mu$). When a bullet of mass $\frac{m}{2}$ strikes horizontally, and get embedded in it, the block moves a distance $d$ before coming to rest. The initial velocity of the bullet is $k\sqrt{2\mu gd}$, then the value of $k$ is