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

Question

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

TestHub · Accepted Answer

tan 4 θ ​ = u + 2 u ​ c o s θ 2 u ​ s i n θ ​ ⇒ sin 4 θ ​ + 2 1 ​ sin 4 θ ​ cos θ = 2 1 ​ sin θ cos 4 θ ​ ∴ 2 sin 4 θ ​ = sin 4 3 θ ​ = 3 sin 4 θ ​ − 4 sin 3 4 θ ​ ∴ sin 2 4 θ ​ = 4 1 ​ ⇒ 4 θ ​ = 3 0 ∘ or θ = 12 0 ∘

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