$\left(F_{1}-F_{2}\right)=\left(\frac{330}{330-V}\right) \times 500-\left(\frac{330}{330+V}\right) \times 500$

Substitute $3$ for $\left(F_{1}-F_{2}\right)$

$3=\left(\frac{330}{330-V}\right) \times 500-\left(\frac{330}{330+V}\right) \times 500$

$=\frac{500}{330^{2}-V^{2}} \times 2 V \times 330$

Here $V^{2}<<330^{2}$ so,

$30=\frac{500 \times 330 \times 2 V}{330^{2}}$

$V=\frac{3}{2}\left(\frac{330}{500}\right)$

$\approx 1 m / s$

Further simplify the above