\(v \sin 60^{\circ}=u \sin 30^{\circ}\)
Components of velocity normal to the plane are related to each other
\(v \cos 60^{\circ}= eu \left(\cos 30^{\circ}\right)\)
\(\Rightarrow \cot 60^{\circ}= e \cot 30^{\circ}\)
\(\Rightarrow e =\frac{\cos 60^{\circ}}{\cot 30^{\circ}}\)
\(\Rightarrow e -\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}} \Rightarrow e =\frac{1}{3}\)