A ball of mass $m$ approaches a wall of mass $M$$\left(\gg m\right)$ with speed $4\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ along the normal to the wall. The speed of wall is $1\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ towards the ball. The speed of the ball after an elastic collision with the wall will be,

Two blocks $A$ and $B$, each of mass $m$,are connected to a massless spring of natural length $L$ and spring constant $K$. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length as shown in the figure. A third identical block $C$, also of mass $m$, moves on the floor with speed $v$ along the line joining $A$ and $B$ and collides elastically with $A$. Then,

A particle of mass $m$ is given initial speed $u$ as shown in the figure. It transfers to the fixed inclined plane without a jump, that is, its trajectory changes sharply from the horizontal line to the inclined line. All the surfaces are smooth and $90°\ge \theta >0°$. Then, the height to which the particle shall rise on the inclined plane (assuming the length of the inclined plane to be very large),