Motion in plane practice · Medium

Position of a particle in a rectangular coordinate system is $(3,2,5)$. Then, its position vector will be:

A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with velocity v. While rising up the velocity of the mass after t seconds will be

The sum of magnitude of two forces acting at a point is $16N$ and their resultant $8\sqrt 3 \,\,N$ is at ${90^0}$ with the force of smaller magnitude. The two forces $\left( {in\,\,N} \right)$ are

Eighteen forces each equal to 10 N act on a particle simultaneously, at an angle $20^{\circ}$ with the next one. If one force is removed, then the resultant of remaining forces is

Which of the following is constant in a projectile motion?

The time of flight of a projectile on an upward inclined plane depends upon

If unit vectors $\hat{a}$ and $\hat{b}$ are inclined at angle $\theta$, then $|\hat{a}-\hat{b}|=$

Two particles are projected in air with same speed $u$ at angle $\theta_1$ and $\theta_2$ (both acute) to the vertical, respectively. If the maximum height reached by the first particle is equal to that of second, then which of the following is correct?

($T_1$ and $T_2$ are time of flight of two particles respectively)

A boat is moving with velocity $(4 \hat{i}+6 \hat{j}) \mathrm{m} / \mathrm{s}$ with respect to ground. The water in the river is moving with $(-3 \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}$ with respect to ground. The velocity of boat with respect to water is

Which of the following statements is/are incorrect?
(i) A scalar quantity is the one that is conserved in a process.
(ii) A scalar quantity is the one that can never take negative values.
(iii) A scalar quantity has the same value for observers with different orientations of the axes.

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\overrightarrow{{A}}+\overrightarrow{{B}}|=|\overrightarrow{{A}}-\overrightarrow{{B}}|$. The angle between the two vectors is

At the highest point on the trajectory of a projectile, its

Assertion : The trajectory of projectile is quadratic in y and linear in x.
Reason : y component of trajectory is independent of x - component.

If $\vec{A}$ is perpendicular to $\vec{B}$, then choose the correct option:

If two vectors $\bar A = 2\hat i - 2\hat j + \hat k\,\,{\text{and }}\,\bar B = 2\hat i + 6\hat j - m\hat k$ are perpendicular to each other, then the value of $m$ is

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Two identical balls A and B thrown with same velocity ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height ${h_1}$ and ${h_2}$ respectively, then $R = 4\sqrt {{h_1}{h_2}}$
Reason R: Product of said heights.
${h_1}{h_2} = \left( {\frac{{{u^2}{{\sin }^2}\theta }}{{2g}}} \right).\left( {\frac{{{u^2}{{\cos }^2}\theta }}{{2g}}} \right)$ Choose the correct answer:

In an oblique projectile motion if the velocity of projection is increased by 2%, the percent increase in horizontal range will be

During projectile motion, the horizontal
velocity

Given $\theta$ is the angle between $\mathrm{\vec A}\,and\,\mathrm{\vec B}$. Then $\left| {\hat A \times \hat B\;} \right|$ is equal to

Magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors, under vector addition, fails to give a resultant vector of magnitude $3 {~ c m}$ ?

The two vectors $\overrightarrow{{A}}$ and $\overrightarrow{{B}}$ are drawn from a common point and $\overrightarrow{{C}}=\overrightarrow{{A}}+\overrightarrow{{B}}$, then angle between $\vec{A}$ and $\vec{B}$ is

(1) $90^{\circ}$ if $\mathrm{C}^2=\mathrm{A}^2+\mathrm{B}^2$

(2) greater than $90^{\circ}$ if $\mathrm{C}^2<\mathrm{A}^2+\mathrm{B}^2$

(3) greater than $90^{\circ}$ if $\mathrm{C}^2>\mathrm{A}^2+\mathrm{B}^2$

(4) less than $90^{\circ}$ if $\mathrm{C}^2>\mathrm{A}^2+\mathrm{B}^2$

Correct options are-

In the case of an oblique projectile, the velocity is perpendicular to acceleration

Assertion: To cross the river in minimum time, swimmer should swim in a direction perpendicular to the water current.
Reason: In this case river flow helps to cross the river.

If $\mathrm{\vec A}\mathrm{.\vec B} = 0\,and\,\,\mathrm{\vec A} \times \mathrm{\vec B} = 1$, then $\mathrm{\vec A}\;\,and\,\mathrm{\vec B}$ are

A body is projected from the earth at angle ${30^0}$ with the horizontal with some initial velocity. If its range is 20 m, the maximum height reached by its is (in metre )

A body of mass $m$ is thrown at angle $\theta$ with horizontal from ground with initial velocity $v$. Find the angle of projection at a point where -

1. Velocity is half of initial velocity.

2. Velocity is $\frac{\sqrt{3}}{2}$ times of initial velocity

Assertion: In a projectile motion, the acceleration is constant in both magnitude and direction but the velocity changes in both magnitude and direction.
Reason: When a force or acceleration is acting in an oblique direction to the direction of velocity, then both magnitude and direction of the velocity may be changed.

A particle is projected in XY plane with Y-axis along vertical, the point of projection is origin. The equation of the path is y= $\sqrt 3 \times - \frac{g}{2}{ \times ^2}$. Where X and Y are in metres. The speed of
projection in $m{s^{ - 1}}$ is

A force of $8 {~N}$ makes an angle $30^{\circ}$ with $X$-axis. Find the $x$ and $y$ components of the force.

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a