A particle at a height $h$ from the ground is projected with an angle $30°$ from the horizontal. It strikes the ground making an angle $45°$ with the horizontal. It is again projected from the same point with the same speed, but with an angle of $60°$ with the horizontal. Find the angle it makes with the horizontal when it strikes the ground.

A projectile is fired at an angle $\theta$ with the horizontal. Find the condition under which it lands perpendicular on an inclined plane of inclination $\alpha$ as shown in the figure.

Three particles$P, Q$ and $R$ are placed as per the given figure. Masses of $P\mathit{,}\mathit{ }Q$ and $R$ are $\sqrt{3 m}, \sqrt{3 m}$ and $m$ respectively. The gravitational force on a fourth particle $S$ of mass $m$ is equal to

The velocity of end $A$ of rigid rod placed between two smooth vertical walls is $u$ along vertical direction. Find out the velocity of end $B$ of that rod, when it slips down.Rod always remains in contact with the vertical wall and also find the velocity of centre of mass of the rod. Also find equation of path of centre of rod.

A $3.0 \mathrm{kg}$ mass is moving in a plane with its $x$ and $y$ coordinates given by $x=5t^2–1$ and $y=3t^3+2$, where $x$ and $y$ are in meters and $t$ is in second. Find the magnitude of the net force acting on this mass at $t=2 \sec$.

There is an inclined surface of inclination $\mathrm{\theta }=30º$. A smooth groove is cut into it forming angle $\alpha$ with $AB$. A steel ball is free to slide along the groove. If the ball is released from the point $O$ at top end of the groove, the speed when it comes to $A$ is $[g=10 {\mathrm{ms}}^{-2}]$

A cuboidal car of height $3 \mathrm{m}$ is slipping on a smooth inclined plane. A bolt released from the roof of car from centre of roof $\left(P\right)$ then distance from centre of roof where bolt hits the floor with respect to car is

A car starts from $P$ and follows the path as shown in the figure. Finally, car stops at $R$. Find the distance travelled and displacement of the car if $a=7 \mathrm{m}$, $b=8 \mathrm{m}$ and $r=\frac{11}{\pi } \mathrm{m}$? Take $\pi =\frac{22}{7}$. The given curved paths are semicircular.