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Q.

A body is projected upwards from level ground with certain speed at an angle θ with horizontal such that at half the maximum height, the velocity vector makes angle 45° with horizontal. Find the value of tan2θ.

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answer is 2.

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Detailed Solution

tan⁡ϕ=vyvx=u2sin2⁡θ−2ghucos⁡θtan⁡45∘=u2sin2⁡θ−2g12u2sin2⁡θ2gucos⁡θu2cos2⁡θ=u2sin2⁡θ2tan2⁡θ=2
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