A Twisted Move.

Two particles $A$ & $B$ are placed at points $(-10\sqrt{3},0)$ & $(-8\sqrt{3},50)$ respectively in space. Particle $A$ is given a velocity of $20ms^{-1}$ in X-Y plane at an angle of $30^{\circ}$ anticlockwise from positive Y-axis & particle $B$ is given a velocity of $20\sqrt{3}ms^{-1}$ in the same plane and at an angle of $60^{\circ}$ clockwise from negative Y-axis.

Instead of traveling in a straight line, due to some force, these two particle travel in separate parabolic path whose equation are $\sqrt{3}y^2-30y=30\sqrt{3}x+900$ & $y^2-10(10-3\sqrt{3})y=30x+1740\sqrt{3}-2500$ respectively.

Find the minimum separation (in metre) between those two particles.

Try more from my set Classical Mechanics Problems .