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

$A$ particle is projected from the horizontal making an angle of $53^{\circ}$ with an initial velocity of $100\,m/s$. The time taken by the particle to make an angle of $45^{\circ}$ with the horizontal is $.........\,s$.

$A$ boy throws a ball with a velocity $V_0$ at an angle $\alpha$ to the ground. At the same time,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

$A$ body of mass $100 \, g$ is projected at an angle of $30^\circ$ with the horizontal with a velocity of $20 \, m \, s^{-1}$. What is the change in its momentum at the maximum height in $kg \, m \, s^{-1}$?

In projectile motion,the modulus of the rate of change of velocity is:

$A$ particle is projected from the ground with some initial velocity making an angle of $45^{\circ}$ with the horizontal. If it reaches a height of $7.5 \ m$ above the ground, while it travels a horizontal distance of $10 \ m$ from the point of projection, then the initial speed of the particle is (assume, $g=10 \ m/s^2$): (in $m/s$)