# Closest Approach

There are two identical particles (mass = $$1 \text{ kg}$$, charge = $$+10^{-4} \text{ C}$$) positioned on the $$x$$-axis. Both charges are free to move.

Particle 1 is initially at $$(x = -1 \text{ m})$$ with a speed of $$10 \text{ m/s}$$ in the $$+x$$ direction.

Particle 2 is initially at rest at $$(x = 0 \text{ m})$$.

In meters, to 3 decimal places, what is the minimum distance that ever separates the two particles?

Note: The Coulomb constant is $$9 \times 10^{9} \text{ N m}^{2} / \text{ C}^{2}$$

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