A particle has two velocities of equal magnitude inclined to each other at an angle $ heta$. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then $ heta$ is

Question

A particle has two velocities of equal magnitude inclined to each other at an angle $	heta$. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then $	heta$ is

Aicharya · Accepted Answer

$	an \frac{	heta}{4}=\frac{\frac{u}{2} \sin 	heta}{u+\frac{u}{2} \cos 	heta}$ $\Rightarrow \sin \frac{	heta}{4}+\frac{1}{2} \sin \frac{	heta}{4} \cos 	heta=\frac{1}{2} \sin 	heta \cos \frac{	heta}{4}$ $	herefore 2 \sin \frac{	heta}{4}=\sin \frac{3 	heta}{4}=3 \sin \frac{	heta}{4}-4 \sin ^3 \frac{	heta}{4}$ $	herefore \sin ^2 \frac{	heta}{4}=\frac{1}{4} \Rightarrow \frac{	heta}{4}=30^{\circ}$ or $	heta=120^{\circ}$

A particle has two velocities of equal magnitude inclined to each other at an angle $\theta$. If one of them…

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