$A$ projectile is fired with a velocity of $21 \, m/s$ at an angle of $\beta = 60^o$ with the horizontal,up an inclined plane making an angle of $\alpha = 30^o$ with the horizontal. The range $R$ on the incline is ....... $m$.

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 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 $PQ$ =

$A$ body is projected with an initial velocity of $10 \,m/s$ from the base of an inclined plane as shown in the figure. If the angle of projection with the horizontal is $60^{\circ}$ and the inclination of the plane is $30^{\circ}$, then the range $R$ along the inclined plane is [take $g=10 \,m/s^2$]:

$A$ particle is projected from a point $A$ with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with the horizontal as shown in the figure. It strikes the plane $BC$ at right angles. The velocity of the particle at the time of collision is

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.