Motion in plane practice · Medium

The sum and difference of two perpendicular vectors of equal length are

The horizontal and vertical displacements of a projectile, as a function of time, are given by $x = 10\,t\,m$ and $y = 12t - 4{t^2}\,m$. The horizontal range of the projectile is

Two particles are projected with same velocity but at angles of projection $25^\circ \,$ and $65^\circ \,$ with horizontal the ratio of their horizontal ranges is

A vector multiplied by the number 0, results into

Assertion (A) : In projectile motion if particle is projected with speed $u$, then speed of particle at height $h$ would be $\sqrt{u^2-2 g h}$.

Reason (R) : If particle is projected with vertical component of velocity $u_y$. Then vertical component at the height $h$ would be $\pm \sqrt{u_y^2-2 g h}$

Let $\vec{a}$ and $\vec{b}$ be two vectors inclined at an angle $\theta$, where $\frac{\pi}{2} < \theta < \pi$.
Statement-I: $|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}| < |\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|$
Statement-II: $|\vec{a}+\vec{b}|^2=a^2+b^2+2\vec{a} \cdot \vec{b}$

If $\vec{a}=(\hat{i}+2 \hat{j}+2 \hat{k})$ and $\vec{b}=(2 \hat{i}+\hat{j}+2 \hat{k})$. The projection of $\vec{b}$ on $\vec{a}$ is

If $\mathrm{\vec A} = 2\hat i + 3\hat j + 6\hat k\,and\,\mathrm{\vec B} = 3\hat i - 6\hat j + 2\hat k$ then vector perpendicular to both $\mathrm{\vec A}\,and\,\mathrm{\vec B}$ has magnitude k times that $\left( {6\hat i + 2\hat j - 3\hat k} \right)$. That k is equal to

Given that A and B are greater than 1. The magnitude of $\left( {\mathrm{\vec A} \times \mathrm{\vec B}} \right)$ can not be

A projectile is thrown with initial velocity $\left( {{V_X}\hat i + {V_Y}\hat j} \right)\,m/s$. If the range of projectile is double the maximum height reached then $\left( {\frac{{{V_y}}}{{{V_x}}}} \right)$ is

A bullet is dropped from the same height when another bullet is fired horizontally. They will hit the ground

The ranges and heights for two projectiles projected with the same initial velocity at angles ${42^\mathrm{o}}\,\,\mathrm{and }\,\mathrm{4}{\mathrm{8}^\mathrm{o}}$ with the horizontal are ${R_1},{R_2}\mathrm{ }\,\,\mathrm{and }\,{H_1},{H_2},$ respectively. Choose the correct option.

The components of a vector along the $x$ and $y$ directions are $\left( {n + 1} \right)$ and 1 respectively. If the coordinate system is rotated by an angle ${60^0}$, then the components changes to $n$ and 3. Find the value of $n$.

If $\mathrm{\vec P} = 2\hat i - 3\hat j + \hat k\,and\,\mathrm{\vec Q} = 3\hat i - 2\hat j,\,then\,\mathrm{\vec P}\mathrm{.\vec Q}$ is

For a projectile thrown into space with a speed v, the horizontal range is $\frac{{\sqrt 3 {v^2}}}{{2\mathrm{g}}}.$ The vertical range is $\frac{{{v^2}}}{{8\mathrm{g}}}$. The angle which the projectile makes with the horizontal initially is

If $|{A} \times {B}|=\sqrt{3} {A} \cdot {B}$, then the value of $|{A}+{B}|$ is

The two vectors have magnitudes 3 and 5 . If angle between them is $60^{\circ}$, then the dot product of two vectors will be :-

Given that $\mathrm{\vec A} + \mathrm{\vec B} + \mathrm{\vec C} = 0$. Out of three vectors, two are equal in magnitude and the magnitude of third vector is&nbsp;$\sqrt 2$ times that of either of the two having equal magnitude. Then the angles between vectors are given by

$(\vec{A}-\vec{B}) \times(\vec{A}+\vec{B})=$

A particle is projected with speed $20 \mathrm{~ms}^{-1}$ at an angle $30^{\circ}$ with horizontal. After how much time the angle between velocity and acceleration will be $90^{\circ}$

Which of the following sets of vectors given below may have zero resultant?

The range $R$ of projectile is same when its maximum heights are $h_1$ and $h_2$. What is the relation between $R$ and $h_1$ and $h_2$

Assertion: The trajectory of an object moving under constant acceleration due to gravity can be a straight line or parabola.
Reason: Initial conditions affect the motion of the object.

I. Pressure
II. Temperature
III. Momentum
IV. Work
Which of the following physical quantities are scalars?

From the top of a tower, a ball A is dropped and another ball B is thrown horizontally at the same time. Which ball strikes the ground first?

Statement I : In order to hit a target, a man should point his rifle in the same direction as the target.

Statement II : The horizontal range of bullet is dependent on the angle of projection with the horizontal.

If $\overrightarrow {{a_1}}$ and $\overrightarrow {{a_2}}$ are two non collinear unit vectors inclined at ${60^0}$ to each other then the value of $\left( {\overrightarrow {{a_1}} - \overrightarrow {{a_2}} } \right).\left( {\overrightarrow {2{a_1}} + \overrightarrow {{a_2}} } \right)$

The resultant of forces $\overrightarrow {{F_1}} = 4\hat i - 3\hat j$ and $\overrightarrow {{F_2}} = 6\hat i + 8\hat j\,$ is

Assertion: The maximum possible height attained by the projected body is $\frac{{{u^2}}}{{2g}}$ where $u$ is the velocity of projection
Reason : To attain the maximum height, body is thrown vertically upwards.

A bomb is dropped from an aeroplane moving horizontally at constant speed. If air resistance is neglected, then the bomb