$A$ 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 $g=10\,m/s^2$).

$A$ 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:

$A$ 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.

$A$ plane is inclined at an angle $\alpha = 30^o$ with respect to the horizontal. $A$ particle is projected with a speed $u = 2 \, m/s$ from the base of the plane,making an angle $\theta = 15^o$ with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to ........ $cm$ (Take $g = 10 \, m/s^2$)

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 $\text{ m}$)

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 ......... $km$.