1.A projectile is launched up an inclined plane of inclination $\alpha=30^\circ$ with initial velocity $u=30\text{ m/s}$ at an angle $\beta=30^\circ$ relative to the incline. Find the range along the incline.
2.A particle moves in x-y plane with position coordinates $x(t) = R\cos(\omega t)$ and $y(t) = R\sin(\omega t)$. Prove that velocity is perpendicular to position vector.
3.Two projectiles are thrown simultaneously from the top of a tower of height $H$ with speeds $u_1$ and $u_2$ horizontally in opposite directions. Find distance between them when their velocities become perpendicular.
