A body starts falling freely from height $\mathrm{H}$ hits an inclined plane in its path at height $\mathrm{h}$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{\mathrm{H}}{\mathrm{h}}$ for which the body will take the maximum time to reach the ground is______.

Two bodies $A$ and $B$ collide as shown in Fig. $(i)$ and $(ii)$ Which statement is true ?

Two identical balls $A$ and $B$ having velocities of $0.5\, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

A body $x$ with a momentum $p$ collides with another identical stationary body $y$ one dimensionally. During the collision $y$ gives an impulse $J$ to body $x$. Then coefficient of restitution is

A tennis ball is released from height $h $ above ground level. If the ball makes inelastic collision with the ground, to what height will it rise after third collision

A ball of mass $200\,g$ rests on a vertical post of height $20\,m$. A bullet of mass $10\,g$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of initial velocity of the bullet will be $............m/s$ (if $\left.g =10 m / s ^2\right)$