A bullet is fired from the bottom of the inclined plane at angle $\mathrm{\theta }=37°$ with the inclined plane. The angle of inclination is $30°$ with the horizontal. Find the position of the maximum height of the bullet from the inclined plane.

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.