A projectile is fired at an angle $\mathrm{\theta }$ with the horizontal. Find the condition under which it lands perpendicular on an inclined plane of inclination $\alpha$ as shown in the figure.

A particle $A$ moves along a circle of radius $R=50 \mathrm{cm}$ so that its radius vector $r$ relative to the fixed point $O$ (figure) rotates with the constant angular velocity $\mathrm{\omega }=0.40 \mathrm{rad} {\mathrm{s}}^{-1}$. Then modulus $v$ of the velocity of the particle, and the modulus $a$ of its total acceleration will be

Two particles $A$ and $B$ move with velocities $v_1$ and $v_2$, respectively, along with the $x$ and $y$ axis. The initial separation between them is $d$, as shown in the figure. Find the least distance between them during their motion.

Which of the following statements are correct?