Motion in a Plane
Which of the following is a vector quantity?
The angle between two vectors $\vec{A}$ and $\vec{B}$ is given by $\theta$. What is the scalar product (dot product) of these two vectors?
What is the direction of the cross product of two vectors $\vec{A}$ and $\vec{B}$ lying in the plane of the paper?
At what angle of projection is the horizontal range of a projectile maximum for a given initial velocity?
The path of a projectile thrown with an initial velocity in a vertical plane is a:
What is the centripetal acceleration of a body moving with a constant speed $v$ in a circle of radius $r$?
If the magnitude of the sum of two vectors is equal to the magnitude of their difference, what is the angle between them?
The maximum range of a projectile is $100\text{ m}$. What is the maximum height reached by it for this launch condition?
Which of the following remains constant during the flight of an ideal projectile in air (neglecting air resistance)?
If unit vectors $\hat{i}$ and $\hat{j}$ are along the x and y axes respectively, what is the value of $\hat{i} \cdot \hat{j}$?
What is the value of $\hat{i} \times \hat{i}$?
The time of flight $T$ of a projectile with initial velocity $u$ and projection angle $\theta$ is given by:
If an object moves along a curved path, its acceleration vector:
The position vector of a particle is given by $\vec{r} = 3t \hat{i} + 4t^2 \hat{j}$. What is the magnitude of its velocity at $t = 1\text{ s}$?
If vectors $\vec{A} = 2\hat{i} + 3\hat{j}$ and $\vec{B} = x\hat{i} + 6\hat{j}$ are parallel to each other, the value of $x$ is:
Rain is falling vertically downwards with a speed of $30\text{ m/s}$. A woman rides a bicycle with a speed of $10\text{ m/s}$ from north to south. What is the apparent velocity of rain relative to the woman?
What is the angle between vectors $(\vec{A} + \vec{B})$ and $(\vec{A} \times \vec{B})$?
A stone is tied to a string of length $L$ and whirled in a horizontal circle with a constant angular velocity $\omega$. What is the magnitude of the acceleration of the stone?
If the scalar product of two vectors is equal to $\sqrt{3}$ times their vector product, what is the angle between the two vectors?
Which of the following sets of three concurrent forces acting in a plane can possibly be in equilibrium?