A particle is projected with velocity $\vec{v} = (6\hat{i} + 8\hat{j})$ m/s. If $g = 10 m/s^2$, the radius of curvature of its trajectory at the highest point is:

A vector $\vec{A}$ has magnitude $10$ and makes an angle of $30^\circ$ with the positive x-axis. What are the x and y components of $\vec{A}$?

The angular velocity of a rotating body is $\mathop \omega \limits^ o = 4\,\widehat {\rm{i}}{\rm{ + }}\widehat {\rm{j}}{\rm{ - 2}}\widehat {\rm{k}}$. The linear velocity of the body whose position vector $2\widehat {\rm{i}}{\rm{ + 3}}\widehat {\rm{j}}{\rm{ - 3}}\widehat {\rm{k}}$ is

A vector has a magnitude of 5 units and is directed along the positive x-axis. What are its components?

The angular velocity of a rotating body is $\mathop \omega \limits^ o = 4\,\widehat {\rm{i}}{\rm{ + }}\widehat {\rm{j}}{\rm{ - 2}}\widehat {\rm{k}}$. The linear velocity of the body whose position vector $2\widehat {\rm{i}}{\rm{ + 3}}\widehat {\rm{j}}{\rm{ - 3}}\widehat {\rm{k}}$ is

If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{j}-4\hat{i}+\alpha\hat{k}$, then the value of $\alpha$ is:

A projectile is launched with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the vertical component of its velocity at the highest point of its trajectory?

\mathop {{\rm{ }}A}\limits^ -   = \mathop {{\rm{ }}B}\limits^ -   + \mathop {{\rm{ }}C}\limits^ -   and the magnitudes of \mathop {{\rm{ }}A}\limits^ -  ,\mathop {{\rm{ }}B}\limits^ -  ,\mathop {{\rm{ }}C}\limits^ -   are 5, 4 and 3 units respectively, the angle between \mathop {{\rm{ }}A}\limits^ -  \mathop {{\rm{ }}C}\limits^ -   is:

A child travelling in a train throws a ball outside with a speed V. According to a child who is standing on the ground, the speed of the ball is

The angular velocity of a rotating body is $\mathop \omega \limits^ o = 4\,\widehat {\rm{i}}{\rm{ + }}\widehat {\rm{j}}{\rm{ - 2}}\widehat {\rm{k}}$. The linear velocity of the body whose position vector $2\widehat {\rm{i}}{\rm{ + 3}}\widehat {\rm{j}}{\rm{ - 3}}\widehat {\rm{k}}$ is

A vector $\mathbf{A}$ has components (3, 4). What is its magnitude?