# A Twisted Move.

Calculus Level 5

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.

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