A motorboat is to reach at a point $30°$ upstream on the other side of a river flowing with velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of the motorboat with respect to water is $5\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$. The driver should steer the boat at an angle

In the figure, the angle of inclination of the inclined plane is $30°$. Find the horizontal velocity $V_0$ so that the particle hits the inclined plane perpendicularly.

Two particles $A$ and $B$ are placed as shown in the figure.The particle $A$ on the top of tower, is projected horizontally with a velocity $u$ and particle $B$ is projected along the surface towards the tower, simultaneously. If both particles meet each other, then the speed of projection of particle $B$ is [ignore any friction]

A projectile is fired with a velocity $v$ at right angle to the slope inclined at an angle $\mathrm{\theta }$ with the horizontal. The range of the projectile along the inclined plane is