$A$ projectile is projected at an angle of $30^{\circ}$ from the horizontal with an initial velocity $u$. If the range of the projectile is $R$,what will be the range if the projectile is projected at an angle of $60^{\circ}$ with the same initial velocity?

$A$ ball of mass $160 \, g$ is thrown up at an angle of $60^{\circ}$ to the horizontal at a speed of $10 \, m/s$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly $\left(g=10 \, m/s^{2}\right)$ (in $kg \cdot m^{2}/s$).

$A$ particle has an initial velocity of $(\hat{i} + \hat{j}) \, m/s$ and an acceleration of $(\hat{i} + \hat{j}) \, m/s^2$. Its speed after $10 \, s$ will be:

Four particles $A, B, C$ and $D$ are moving with constant speed $v$ each. At the instant shown,the relative velocities of $A$ with respect to $B, C$ and $D$ are in the directions:

The second's hand of a watch has a length of $6\,cm$. The speed of the end point and the magnitude of the difference of velocities at two perpendicular positions will be:

At any time $t$,the coordinates of a moving particle are $x = at^2$ and $y = bt^2$. The speed of the particle is