$A$ particle is projected with velocity $u$ at an angle $\theta$ with the horizontal. What is the change in its velocity at the maximum height?

$A$ body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

$A$ particle $P$ is projected with velocity $u_1$ at an angle of $30^\circ$ with the horizontal. Another particle $Q$ is projected vertically upwards with velocity $u_2$ from the point directly below the maximum height of $P$. The condition for the collision of both particles is:

$A$ particle having kinetic energy $K$ is projected at $60^{\circ}$ with the horizontal. The kinetic energy at the highest point is

$A$ projectile is projected at $10 \ m/s$ by making an angle of $60^{\circ}$ to the horizontal. After some time,its velocity makes an angle of $30^{\circ}$ to the horizontal. Its speed at this instant is:

Two guns $A$ and $B$ can fire bullets at speeds $1 \ km/s$ and $2 \ km/s$ respectively. From a point on a horizontal ground,they are fired in all possible directions. The ratio of the maximum areas covered by the bullets fired by the two guns on the ground is