$A$ small ball is projected up a smooth inclined plane with an initial speed of $10 \ m/s$ along a direction at $30^{\circ}$ to the bottom edge of the slope. It returns to the edge after $2 \ s$. The ball is in contact with the inclined plane throughout the process. Find the inclination angle $\theta$ of the plane. (in $^{\circ}$)

Find the time of flight of a projectile thrown horizontally with a speed of $50 \ m/s$ from a long inclined plane which makes an angle of $\theta = 45^{\circ}$ with the horizontal.

$A$ particle falling vertically from a height hits a plane surface inclined to the horizontal at an angle $\theta$ with speed $v_0$ and rebounds elastically. Find the distance along the plane where it will hit the second time.

$A$ particle is projected in air at an angle $\beta$ to a surface which itself is inclined at an angle $\alpha$ to the horizontal (figure).
$(a)$ Find an expression for the range on the plane surface (distance on the plane from the point of projection at which the particle will hit the surface).
$(b)$ Find the time of flight.
$(c)$ Find the angle $\beta$ at which the range will be maximum.

If the time taken by the projectile to reach point $P$ from point $Q$ is $T$,and the velocity at $P$ is perpendicular to the inclined plane,then $PQ$ =

The surface of a hill is inclined at an angle of $30^{\circ}$ to the horizontal. $A$ stone is thrown from the summit of the hill (point $A$) at an initial speed of $10 \text{ m/s}$ at an angle of $60^{\circ}$ to the vertical. If the stone strikes the hill at point $B$ as shown in the figure,the distance between $A$ and $B$ is (Take $g = 10 \text{ m/s}^2$) (in $\text{ m}$)