If the maximum range down an inclined plane is three times the maximum range up the same inclined plane,find the angle of inclination in degrees.

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

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.

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 $\text{ m}$)

$A$ projectile is fired with a velocity $v$ at a right angle to a slope which is inclined at an angle $\theta$ with the horizontal. The expression for the range $R$ along the incline is

$A$ 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.