If the maximum range of a projectile on horizontal ground is $6 \, km$,then the maximum range on an inclined plane with an angle of $30^o$ is ......... $km$.

$A$ 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.

$A$ 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.

$A$ projectile is projected with speed $u$ at an angle of $60^o$ with the horizontal from the foot of an inclined plane. If the projectile hits the inclined plane horizontally,the range on the inclined plane will be:

$A$ man standing on a hill top projects a stone horizontally with speed $v_0$ as shown in the figure. Taking the coordinate system as given in the figure,the coordinates of the point where the stone will hit the hill surface are:

$A$ projectile is launched with a speed of $10\,m/s$ at an angle of $60^{\circ}$ with the horizontal from a sloping surface of inclination $30^{\circ}$. The range $R$ is $........\,m$ (Take $g=10\,m/s^2$).