BM Sharma Solutions for Chapter: Motion in Two Dimensions, Exercise 3: DPP

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

A ball is projected with a velocity $u$ at a right angle to the inclined plane which is inclined at an angle $\alpha$ with the horizontal. The distance $x$ along the inclined plane that it will travel before again striking the slope is

A stone is projected from point $A$, $60°$ with the horizontal as shown. The fixed inclined surface makes an angle $30°$with the horizontal. The stone lands at $B$ after time $t$. Then, the distance $AB$ is equal to

A particle is projected from the surface of the inclined plane with speed $u$ and at an angle $\theta$ with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in the vertical direction. Starting from projection, find the time taken by the particle to reach maximum height (neglect time of collision).

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A particle is projected from a point $P(2,0,0) \mathrm{m}$ with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$ making an angle $45°$ with the horizontal. The plane of projectile motion passes through a horizontal line $PQ$ which makes an angle of $37°$ with positive $x$-axis, $xy$ plane is horizontal. The coordinates of the point where the particle will strike the line $PQ$ is

A particle is projected from point $A$ on plane $AB,$ so that $AB=\frac{2u^2 \tan \left(\theta \right)}{g\sqrt{3}}$ in the figure as shown. If $u$ is the velocity of projection, find angle $\mathrm{\theta }$.

On an inclined plane, two particles $A$ and $B$ are projected with the same speed at the same angle with the horizontal, particle $A$ down and particle $B$ up the plane. If the ratio of time of flight of $A$ and $B$ is $\cot \theta$ where $\theta$ is the angle at which  $B$ 

Two balls are thrown from an inclined plane at an angle of projection $\mathrm{\alpha }$ with the plane, one up the incline plane and the other down the incline as shown in the figure. If $R_1$ and $R_2$ are their respective ranges, then ($T_1$ and $T_2$ are times of flight in the two cases, respectively)