Basics of Motion in a Plane

A bus is moving on a straight road towards north with a uniform speed of  $50 \mathrm{km} {\mathrm{h}}^{-1}$  turns through  $90°$ anticlockwise. If the speed remains unchanged after turning , the increase in the velocity of bus in the turning process is:

Three forces starts acting simultaneously on a particle moving with velocity $\overrightarrow{v}.$ These forces are represented in magnitude and direction by the three sides of a triangle $ABC$ (as shown). The particle will now move with velocity

The trajectory of a projectile in a vertical plane is $y=ax-b{x}^2,$ where $a, b$ are constants, and $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. Find the maximum height $H_{\max }$ attained by the projectile and the angle of projection from the horizontal.

A ball is projected from ground with $20 \mathrm{m} {\mathrm{s}}^{-1}$at$45 °$ with horizontal. A wall is of $25 \mathrm{m}$ height at distance of$10 \mathrm{m}$ from the projection point. The ball will hit the wall at height of

A vector in $x-y$ plane makes an angle of ${30}^{\mathrm{o}}$ with $y$-axis. The magnitude of $y$-component of vector is $2\sqrt{3}$. The magnitude of $x$-component of the vector will be :

When vector $\overrightarrow{A}=2\hat{i}+3\hat{j}+2\hat{k}$ is subtracted from vector $\overrightarrow{B}$, it gives a vector equal to $2\hat{j}$. Then the magnitude of vector $\overrightarrow{B}$ will be:

Two forces having magnitude $\mathrm{A}$ and $\frac{\mathrm{A}}{2}$ are perpendicular to each other. The magnitude of their resultant is:

If $\left|\overrightarrow{r_A}\right|=3 \mathrm{m}$ and $\left|{\overrightarrow{r}}_B\right|=5 \mathrm{m}$ then find the displacement from A to B

If y-component of a force acting in x-y plane is $2\sqrt{3} \mathrm{N}$. Then the x- component will be

If $\overrightarrow{A}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $\overrightarrow{A}-\overrightarrow{B}=2\hat{\mathrm{j}}$, then find $\left|\overrightarrow{B}\right|$.

Two forces of magnitude $A$ and $\frac{A}{2}$ act perpendicular to each other. The magnitude of the resultant force is equal to

If momentum of a particle is given by $\overrightarrow{p}=10\sin \left(2t\right)\hat{\mathrm{i}}+10\cos \left(2t\right)\hat{\mathrm{j}}$

a) Find the magnitude of force at any time.

b) Find the angle between momentum and force.

 The projection of the vector $\overrightarrow{AB}$ on the directed line $l$, if angle $\theta =\pi$ will be

If $\overrightarrow{A}=(2\hat{i}+3\hat{j}-\hat{k}) \mathrm{m}$ and $\overrightarrow{B}=(\hat{i}+2\hat{j}+2\hat{k}) \mathrm{m}$. The magnitude of component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B }$will be _____$\mathrm{m}$

The resultant of two vectors is perpendicular to one of them and has the magnitude $4 \mathrm{m}$. If the sum of the magnitude of two vectors is $8 \mathrm{m}$ then their respective magnitude are

An aeroplane has to reach $A$to $B$ and back again along straight line. The speed of aeroplane with respect to wind is $v$. The wind blows perpendicular to line$AB$ with speed $u$. The distance between $A$and $B$ is $l$. The total time for the round trip is
 

Find Resultant of all Vectors.

Four particles lie initially at the corners of a square of side length$L$. All the particles start to move with speed$v.$ $A$ moves towards $B$,$B$ moves towards $C$,$C$ moves towards$D$and $D$ moves towards $A$. The distance covered by a particle till they meet, is