Determine the separation at which two equal charges of 1.0 C each...

The electrostatic force between two charges is given by Coulomb's law:

$F = \dfrac{1}{4\pi\epsilon_0} \dfrac{q_1 q_2}{r^2}$

The weight of the person is given by:

$W = mg$

Equating the electrostatic force to the weight of the person:

$\dfrac{1}{4\pi\epsilon_0} \dfrac{q_1 q_2}{r^2} = mg$

Substituting the given values ($q_1 = q_2 = 1.0 \text{ C}$, $m = 50 \text{ kg}$, $g = 9.8 \text{ m/s}^2$, $\dfrac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2$):

$\dfrac{9 \times 10^9 \times 1.0 \times 1.0}{r^2} = 50 \times 9.8$

$\dfrac{9 \times 10^9}{r^2} = 490$

$r^2 = \dfrac{9 \times 10^9}{490} = \dfrac{900}{49} \times 10^6$

$r = \dfrac{30}{7} \times 10^3 \approx 4.28 \times 10^3 \text{ m}$

Rounding to two significant figures, we get $4.3 \times 10^3 \text{ m}$.