Motion in plane practice · Medium

A man is swimming with speed 10 km/h in still water crosses a river of width 1 km along the shortest path in 10 minutes. The velocity of river flow is

If the range of oblique projectile is ${R}$, then its K.E. is maximum after (from start) a displacement equal to

There are two values of time for which a projectile is at the same height, The sum of these two times is equal to ($T =$ time of fight of the projectile)

What is the angle between $\mathbf{P}$ and the cross product of $(\mathbf{P}+\mathbf{Q})$ and $(\mathbf{P}-\mathbf{Q})$ ?

Assertion: The sum of squares of cosines of angles made by a vector with $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ axes is equal to unity.
Reason: A vector making $45^{\circ}$ with $\mathrm{X}$-axis must have equal components along $\mathrm{X}$ and $\mathrm{Y}$-axes.

A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement-time graph is characterised by

A boat takes two hours to travel 8 km and back in still water. If the velocity of water 4 $\mathrm{km}{\mathrm{h}^{ - 1}}$, the time taken for going ups tream 8km and coming back is

Some persons hire a boat for 4 hours. The river flows at a speed of $5 \mathrm{~km} / \mathrm{hr}$ and the boat moves with speed of $15 \mathrm{~km} / \mathrm{hr}$ relative to the water. How far along the flow direction, they can go if they have to return in 4 hrs?

Which of the following conditions are sufficient and essential for a quantity to be a vector?

If $u$ is the initial velocity of a projectile and $v$ is the velocity at any instant, then the maximum horizontal range $\mathrm{R}_{\mathrm{m}}$ is equal to

Position of a particle at any instant $t$ is given $\vec{r}=3 \hat{i}+2 t^2 \hat{j}+5 \hat{k}$, Its velocity at same instant will be:

A particle is projected upwards with a velocity of $100 \mathrm{~m} / \mathrm{sec}$ at an angle of $60^{\circ}$ with the vertical. Find the time in seconds when the particle will move perpendicular to its initial direction, taking ${g}=10 \mathrm{~m} / \mathrm{sec}^2$

If two non-parallel vectors $\vec{A}$ and $\vec{B}$ are equal in magnitude, then the vectors $(\vec{A}-\vec{B})$ and $(\vec{A}+\vec{B})$ will be

A stone is thrown with a velocity $u$ making an angle $\theta \,$ with the horizontal. The horizontal distance covered by its fall to ground is maximum when the angle $\theta \,$ is equal to

Assertion: A man can cross river of width $d$ in minimum time. On increasing the river velocity, minimum time to cross the river by man will remain unchanged.
Reason: As velocity of a river is perpendicular to its width so time to cross the river is independent of velocity of river.

The maximum range of a projectile is $100 \mathrm{~m}$ The maximum height reached by it is

A ball is projected horizontally from the top of a tower with a velocity $v_0$. It will be moving at an angle of $60^{\circ}$ with the horizontal after time,

At the top of trajectory of a projectile, the acceleration is

The equation of trajectory of a projectile in the vertical plane is $y = \left[ {10x - \left( {\frac{5}{9}} \right){x^2}} \right]m$. the horizontal distance covered by the projectile when it reaches the maximum height is $\left[ {g = 10\,\,m{s^{ - 2}}} \right]$

A particle has two equal accelerations in two given directions. If one of the accelerations is halved, then the angle which the resultant makes with the other is also halved. The angle between the accelerations is

$\overrightarrow A$ is a vector quantity such that $\left| {\overrightarrow A } \right| = \,$ non-zero constant. Which of the following expression is true for $\overrightarrow A$?

The lines $\vec{r}=2 \hat{k}+\lambda(3 \hat{i}+2 \hat{j}+\hat{k})$ and $\vec{r}=3 \hat{i}+2 \hat{j}+3 \hat{k}$ $+\mu(6 \hat{i}+4 \hat{j}+2 \hat{k})$ are:

Given that, ${P}+{Q}+{R}=0$. Which of the following statement is true?

Statement-I: Let $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=\hat{i}-\hat{j}$ be two vectors. Angle between $\hat{a}+\hat{b}$ and $\hat{a}-\hat{b}=90^{\circ}$
Statement-II: Projection of $\vec{a}+\vec{b}$ on $\vec{a}-\vec{b}$ is zero.

Two forces whose magnitudes are in the ratio 3:5 give a resultant of 35N. If the angle between them is ${60^\mathrm{o}}$, the magnitude of each force is

The resultant of two forces at right angle is 5N. When the angle between them is ${120^0}$, the resultant is $\sqrt {13}$. Then the force are

Assertion (A): The distance between two floating objects on a river flowing uniformly does not changes with time.

Reason (R): The floating object has the same velocity as that of the river.

If the angle between two forces increases, the magnitude of their resultant

Two bodies are projected from roof with same speed in different directions. If air resistance is not taken into account then

Assertion: Commutative law is followed while vector addition.
Reason: Addition of two vectors maybe done graphically using head-to-tail method or parallelogram method.