Motion in plane practice · Easy

If $a \hat{\mathbf{i}}+b \hat{\mathbf{j}}$ is a unit vector and it is perpendicular to $\hat{\mathbf{i}}+\hat{\mathbf{j}}$, then value of $a$ and $b$ is

If $\left| {\bar A + \bar B} \right| = \left| {\bar A} \right| = \left| {\bar B} \right|\,$, the angle between $\overrightarrow A$ and $\overrightarrow B$ is

In a projectile motion, velocity at maximum height is

If a vector $\vec P$ make angles $\alpha ,\,\beta ,$ and $\gamma$ respectively with the $X,\,\,Y$ and $Z$ axes. Then ${\sin ^2}\alpha \,\, + \,\,{\sin ^2}\beta \,\, + \,\,{\sin ^2}\gamma \,\, =$

A bat and an insect are flying with velocities $\overrightarrow{{V}}_{\mathrm{BG}}$ and $\overrightarrow{{V}}_{\text {IG }}$ respectively with respect to ground (in unit vector $\hat{{i}}, \hat{{j}}$ rotation)

$\vec{V}_{\text {BG }}=3.5 \hat{{i}}+9.2 \hat{{j}}, \overrightarrow{\mathrm{V}}_{\mathrm{IG}}=-2.5 \hat{{i}}+{1 . 8} \hat{{j}}$

Calculate the velocity of the insect with respect to bat.

The vectors $a \hat{i}+2 \hat{j}+6 \hat{k}$ and $2 \hat{i}+2 \hat{j}+6 \hat{k}$ are equal vectors. The value of $a$ is

The vectors sum of two forces is perpendicular to their vector differences in that case. The forces

If $\mathrm{\vec A} = \mathrm{\vec B},$ then which of the following is not correct

$\mathbf{A}$ and $\mathbf{B}$ are two vectors given by $\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ and $\mathbf{B}=2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}$. The magnitude of the component of $\mathbf{A}$ along $\mathbf{B}$ is

For vectors $\overrightarrow A \,$ and $\overrightarrow B \,$ making an angle $\theta$ which one of the following relations is correct

If air resistance is not considered in projectiles, the horizontal motion takes place with

Assertion(A): When $\theta=45^{\circ}$ or $135^{\circ}$, the value of $R$ remains the same, only the sign changes.

Reason(R): $R=\frac{u^2 \sin 2 \theta}{g}$

I.Inprojectilemotion,theanglebetwee instantaneousvelocityvectorandacceleration vector can be anything between 0 to $\pi$ (excluding the limiting case.)

II. In projectile motion, acceleration vector is always pointing vertically downwards. (Neglect air friction).

Which of the following statement(s) is/are correct?

If the resultant of the vector $3\bar i + 4\bar j + 5\bar k$ and $5\bar i + 3\bar j + 4\bar k$ makes an angle $\theta \,$ with x-axis. Then find $\cos \theta$

A scalar quantity is one that

Which one of the following pair cannot be the rectangular components of force vector of 10 N?

The horizontal and vertical components of a force are 3 N and 4 N respectively. Then force is

If $\mathbf{A} \cdot \mathbf{B}=\mathbf{A} \times \mathbf{B}$, then angle between $\mathbf{A}$ and $\mathbf{B}$ is

What is the angle between $\left( {i + j} \right)\,$ and $\left( {\bar k + \bar j} \right)$?

Magnitude of component of vector $2 \hat{i}+6 \hat{k}$ along $y$-axis is

Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is

A ball is projected with kinetic energy $E$ at an angle of $45^\circ$ to the horizontal. At the highest point during its flight, its kinetic energy will be

Statement-I: Angle between $\hat{i}+\hat{j}$ and $\hat{i}$ is $45^{\circ}$.
Statement-II: $\hat{i}+\hat{j}$ is equally inclined to both $\hat{i}$ and $\hat{j}$ and the angle between $\hat{i}$ and $\hat{j}$ is $90^{\circ}$

Which of the following statement is true?

A body throws a ball with a velocity of 15 m/s at an angle of $15^\circ$ with the horizontal. The distance at which the ball strikes the ground is

The angle made by the vector $\vec A = \hat i + \hat j\,$ with y-axis is

A vector is added to an equal and opposite vector of similar nature, forms a

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

If $\bar A = 5i + 7j - 3k$ and $\bar B = 2i + 2j - ak$ are perpendicular vectors. The value of $a$ is

Two particles are projected from the same point with the same speed, at different angles $\theta_1$ and $\theta_2$ to the horizontal. They have the same horizontal range. Their times of flight are $t_1$ and $t_2$ respectively incorrect statement is.