A particle is projected at an angle of elevation $\alpha$ and after $t$ second, it appears to have an angle of elevation $\beta$ as seen from the point of projection. The initial velocity will be

Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation $\alpha =30°, \beta =60°$, respectively (figure). The shots strike an object simultaneously at the same point. If $a=30\sqrt{3} \mathrm{m}$ is the horizontal distance of the object from the cliff, then the height $h$ of the cliff is

figure shows that particle $A$ is projected from point $P$. with velocity $u$ along the plane and simultaneously another particle $B$ with velocity $v$ at an angle $\alpha$ with vertical. The particles collide at point $Q$ on the plane. Then

Two balls are projected from points $A$ and $B$ in vertical plane as shown in figure. $AB$ is a straight vertical line. The balls can collide in mid-air if $\frac{v_1}{v_2}$ is equal to,

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Two particles $P$ and $Q$ are projected simultaneously away from each other from a point $A$ as shown in the figure.

The velocity of $P$ relative to $Q$ in $\mathrm{m} {\mathrm{s}}^{-1}$ at the instant when the motion of $P$ is horizontal is

Two guns on a battleship simultaneously fire two shells at the same speed at enemy ships. If the shells follow the parabolic trajectories shown in the figure, which ship will get hit first?

Two identical balls are set into motion simultaneously from equal heights $h$. While the ball $A$ is thrown horizontally with velocity $v$, the ball $B$ is just released to fall by itself. Choose the alternative that best represents the motion of $A$ and $B$ with respect to an observer who moves with the velocity $\frac{v}{2}$ with respect to the ground as shown in the figure.