$A$ body is projected with velocity $u$ making an angle $\alpha$ with the horizontal. Its velocity when it is perpendicular to the initial velocity vector $u$ is

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\pi / 3$ and its maximum height is $h_1$,then the maximum height of the other will be:

The position vector of a particle moving in a plane is given by $r = a \cos \omega t \hat{i} + b \sin \omega t \hat{j}$,where $\hat{i}$ and $\hat{j}$ are the unit vectors along the rectangular axes $X$ and $Y$; $a$,$b$,and $\omega$ are constants,and $t$ is time. The acceleration of the particle is directed along the vector:

$A$ particle moves with constant angular velocity in a circle. During the motion,its:

$A$ particle moves towards east with a velocity of $5\ m/s$. After $10\ s$,its direction changes towards north with the same velocity. The average acceleration of the particle is:

$A$ projectile of mass $m$ is projected from the ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle comes to rest immediately after the explosion. The ratio of the radii of curvatures of the moving particle just before and just after the explosion is: