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.

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

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 $\text{ m}$)

$A$ particle is projected at an angle of $60^{\circ}$ with a speed of $10\sqrt{3} \text{ m/s}$ from point $A$ as shown in the figure. At the same time,the wedge is made to move with a speed of $10\sqrt{3} \text{ m/s}$ towards the right as shown in the figure. The time after which the particle will strike the wedge is ........ $\text{s}$.

$A$ 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

$A$ 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 ....... $m$.