Motion in plane practice · Medium

$\overrightarrow A ,\,\,\overrightarrow B ,\,\,\overrightarrow C \,$ are three coplanar vectors, then

In ground to ground projectile motion under gravity, which of the following doesn't affect the time of flight?

A bomb is released from a horizontal flying
aeroplane. The trajectory of bomb is

A person sitting in the rear end of the compartment throws a ball towards the front end. The ball follows a parabolic path. The train is moving with velocity of $20 \mathrm{~m} / \mathrm{s}$. A person standing outside on the ground also observes the ball. How will the maximum heights $\left({y}_{{m}}\right)$ attained and the ranges $({R})$ seen by the thrower and the outside observer compare with each other?

Three particles A, B and C are projected from the same point with the same initial speeds making angles ${30^0},{45^0}\,and\,{60^0}$ respectively with the horizontally. Which of the following statements is correct?

If a particle is projected with speed ${u}$ from the ground at an angle $\theta$ with horizontal. Radius of curvature of a point where velocity vector is perpendicular to initial velocity vector is given by

Assertion : When the range of projectile is maximum, the time of flight is the largest.
Reason : Range is maximum when angle of projection is $45^\circ$

A ball rolls off the top of a stairway with horizontal velocity ${v_0}m{s^{ - 1}}$. If the steps are h metre high and w metre wide, the ball will hit the edge of nth step if

If $0.5\hat i + 0.8\hat j + \mathrm{c\hat k}$ is a unit vector, then the value of c is

If ${A}+{B}={C}$ and that ${C}$ is perpendicular to ${A}$. What is the angle between ${A}$ and ${B}$, if $|{A}|=|{C}|?$

If a body is in equilibrium under a set of non-collinear forces, then the minimum number of forces has to be

Choose the correct statement(s) from the following.
I. If speed of a body in a curved path is constant it has zero acceleration
II. When a body moves on a curved path with a constant speed, it has acceleration perpendicular to the direction of motion

If the angle between two non-zero vectors $\mathbf{A}$ and $\mathbf{B}$ is $120^{\circ}$, its resultant $C$ will be

Two bodies are thrown with the same initial velocity of 30 m/s. One at $17^\circ$, other at $73^\circ$ to the horizontal. The sum of the maximum heights reached by them is $[g = 10\,\,m\mathrm{/}{s^2}]$

The minimum number of vectors having different planes which can be added to give zero resultant is

If $\hat{a}+2 \hat{b}$ and $5 \hat{a}-4 \hat{b}$ are perpendicular to each other, find angle between $\hat{a}$ and $\hat{b}$ :-

Statement-I: The cross product of a vector with itself is a null vector.
Statement-II: The cross product of two vectors results is a vector quantity.

If $\vec{A}+\vec{B}=\vec{C}$ and $A^2+B^2=C^2$, then $\vec{A}$ and $\vec{B}$ are perpendicular to each other.

Assertion: In a projectile motion the projectile hits the ground with the same velocity with which it was thrown.
Reason: In a projectile motion horizontal velocity remains same but vertical velocity continuously changes and particle strikes the ground with same vertical velocity with which the particle was thrown in vertical direction.

The sum of two vectors $\mathrm{\vec A}\,and\,\mathrm{\vec B}$ is at right angles to their difference. Then

The resultant of ${\bar P}$ and ${\bar Q}$ is perpendicular to ${\bar P}$. The angle between ${\bar P}$ and ${\bar Q}$ is

Find the vector for which when added to the resultant of $\vec{P}=2 \hat{i}+7 \hat{j}-10 \hat{k}$ and $\vec{Q}=\hat{i}+2 \hat{j}+3 \hat{k}$ gives a unit vector along $\mathrm{X}$-axis.

For the resultant of two vectors $\vec{A}$ and $\vec{B}$ to maximum. The angle between them should be

An aeroplane moving horizontally at a speed of 200 m/s and at a height of $8.0 \times {10^3}\;m$ is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released

The plane which can be formed with the vectors $\overrightarrow a = 3\overrightarrow i - 4\overrightarrow j + 2\overrightarrow k$,$\overrightarrow b = 2\overrightarrow i - \overrightarrow j - 6\overrightarrow k ,\overrightarrow c = 5\overrightarrow i - \overrightarrow {5j} - 4\overrightarrow k$ IS

In the projectile motion of an object, the object reaches its maximum height where its speed is half of initial speed. Then the ratio between range and maximum height of projectile is

Assertion : Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.
Reason : The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

A stone is projected from the ground with velocity $50\mathrm{\;m}{\mathrm{s}^{ - 1}}$ and angle of ${30^0}$. It crosses a wall after 3 s. How far beyond the wall the stone will strike the ground?

The vectors $\mathrm{2\hat i} + 3\mathrm{\hat j} - 2\mathrm{\hat k},\mathrm{\;}5\mathrm{\hat i} + \mathrm{a\hat j} + \mathrm{\hat k}\,\,\,\mathrm{ and } - \mathrm{\hat i} + 2\mathrm{\hat j} + 3\mathrm{\hat k}$ are coplanar when a is

Statement-1: If we want to throw a bottle from a moving train so that danger of being broken on hitting ground is least. We should throw bottle in forward direcrion.
Statement-2: While jumping out from side of a moving carriage it is safer to jump in forwards direction.