A gun of mass$M,$ fires a shell of mass $\mathrm{m}$ horizontally and the energy of explosion is such as would be sufficient to project the shell vertically to a height ' $h$ '. The recoil velocity of the gun is

A block of mass $M$ is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass $2 M$ as shown in figure. The block and the man are resting on a rough wedge of mass $M.$ The whole system is resting on a smooth horizontal surface. The man starts walking towards right while holding the rope in his hands. Pulley is massless and frictionless. Find the displacement of the wedge when the block meets the pulley. Assume wedge is sufficiently long so that man does not fall down.

Two men $\mathrm{A}$ and $\mathrm{B}$ are standing on a plank. $\mathrm{B}$ is at the middle of the plank and $\mathrm{A}$ is at the left end of the plank. The system is initially at rest and masses are as shown in the figure. $\mathrm{A}$ and $\mathrm{B}$ start moving such that the position of $\mathrm{B}$ remains fixed with respect to ground, then $\mathrm{A}$ meets $\mathrm{B}$. Then, the point where $\mathrm{A}$ meets $\mathrm{B}$ is located at,