# 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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