Two particles P and Q are projected simultaneously away from each other from a point A as shown in figure. The velocity of P relative to Q in ms^-1 at the instant when the motion of P is horizontal is

 

Initially : ${\overrightarrow{\mathrm{u}}}_{\mathrm{P}}=20\cos {60}^{\circ }\hat{\mathrm{i}}+20\sin {60}^{\circ }\hat{\mathrm{j}}=10\hat{\mathrm{i}}+10\sqrt{3}\hat{\mathrm{j}}$

$\overrightarrow{{\mathrm{u}}_{\mathrm{Q}}}=20\sqrt{2}\left[\cos {45}^{\circ }(-\hat{\mathrm{i}})+\sin {45}^{\circ }\hat{\mathrm{j}}\right]=-20\hat{\mathrm{i}}+20\hat{\mathrm{j}}$

Initial relative velocity : 

$\overrightarrow{{\mathrm{u}}_{\mathrm{p}/\mathrm{Q}}}={\overrightarrow{\mathrm{u}}}_{\mathrm{p}}-{\overrightarrow{\mathrm{u}}}_{\mathrm{Q}}=30\hat{\mathrm{i}}+(10\sqrt{3}-20)\hat{\mathrm{j}}$

${\mathrm{u}}_{\mathrm{p}/\mathrm{Q}}=\sqrt{{30}^2+(10\sqrt{3}-20{)}^2}=20\sqrt{4-\sqrt{3}} {\mathrm{ms}}^{-1}$

This relative velocity will remain same till both the particles are in air, because relative acceleration is zero.