Given lines \(OA\) and \(OB\) inclined at angle \(\theta\), the line \(AB\) is gotten using cosine rule.
\(|AB|^{2} = |OA|^{2} + |OB|^{2} - 2|OA||OB|\cos \theta\)
\(|AB|^{2} = 4^{2} + 5^{2} - 2(4)(5)\cos 60\)
= \(16 + 25 - 20\)
\(|AB|^{2} = 21 \implies |AB| = \sqrt{21}\)
\(\implies \text{The two particles are} \sqrt{21} m \text{apart in 1 sec}\)
In two seconds, the particles will be \(2\sqrt{21} m\) apart.