A particle is projected on an inclined plane with a speed $u$ as shown in the figure. Find the range of the particle on the inclined plane.
  

There are three paths $a, b$ and $c$ of a projectile projected from point $P$ as shown in figure. Prove that $v_1>v_2$ and $v_3=v_4$. Which path is correct?

Two cars are moving, car $A$ along east and car $B$ is moving along south. Draw the direction of the motion of
(a) car $A$ as seen from car $B$
(b) car $B$ as seen from car $A$

Two cars $A$ and $B$ are moving as shown in the figure. Calculate the relative velocity of $A$ with respect to $B$. Also draw the direction of motion of car $A$ as seen from car $B$.

Ram was riding in a car travelling at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ towards east. Shyam was standing on the sideway when the car passed him. Just before the car passed close to Shyam (when it was north-west of him), Ram threw a banana peel relative to him with velocity ${\overrightarrow{v}}_{\text{Peel, Ram }}=\left[\right(-10)\hat{i}+(-10\left)\hat{j}\right] \mathrm{m} {\mathrm{s}}^{-1}$. Shyam accused that Ram had thrown the banana peel at him. Justify his statement.

A rat is moving down the slant of a wedge of angle of inclination $\mathrm{\theta }$ with a velocity $\overrightarrow{v}$ as shown in the figure. If the wedge moves towards left with a velocity $\overrightarrow{u}$, find

(a) velocity of the rat relative to ground,
(b) value of $\mathrm{\theta }$, if the rate moves vertically downward relative to an observer $G$ fixed with the ground.

A truck is moving a constant velocity of $u=54 \mathrm{km} {\mathrm{h}}^{-1}$. In what direction should a stone be projected up with a velocity of $v=30 \mathrm{m} {\mathrm{s}}^{-1}$, from the floor of the truck, so as to appear at right angles to the truck, for a person standing on earth?

A block slips along an incline of a wedge. Due to the reaction of the block on the wedge, it slips backwards. An observer on the wedge will see the block moving straight down the incline. Discuss how to find the absolute velocity of the block.