$A$ sphere of mass $m$ moving with velocity $u$ undergoes a collision with a stationary sphere of mass $m$. If the coefficient of restitution is $e = 1/2$,what is the ratio of the final velocities of the two spheres?

Ball $A$ of mass $50 \ gm$ and speed $10 \ m/s$ collides with another ball $B$ of mass $10 \ gm$ and speed $15 \ m/s$ travelling in opposite directions. Determine the final speed of ball $B$,if the coefficient of restitution is $\frac{2}{5}$.

$A$ ball falling freely from a height of $4.9 \, m$ hits a horizontal surface. If the coefficient of restitution is $e = \frac{3}{4}$,then the ball will hit the surface for the second time after .............. $s$.

$A$ ball hits the floor and rebounds after an inelastic collision. In this case:

An electron collides with a free molecule initially in its ground state. The collision leaves the molecule in an excited state that is metastable and does not decay to the ground state by radiation. Let $K$ be the sum of the initial kinetic energies of the electron and the molecule,and $p$ be the sum of their initial momenta. Let $K^{\prime}$ and $p^{\prime}$ represent the same physical quantities after the collision. Then,

$A$ ball strikes a smooth horizontal ground at an angle of $45^o$ with the vertical. What cannot be the possible angle of its velocity with the vertical after the collision? (Assume $e \leq 1$ ).