The angle of projection of a particle is measured from the vertical axis as and the maximum height reached by the particle is . Here as function of can be represented as [2025]

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Solution

Q.
The angle of projection of a particle is measured from the vertical axis as $ϕ$ and the maximum height reached by the particle is $h_{m}$ . Here $h_{m}$ as function of $ϕ$ can be represented as [2025]

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Ans.
(3)

$h_{m} = \frac{u^{2} \sin^{2} θ}{2 g}, θ = 90 ° - ϕ$

$\Rightarrow h_{m} = \frac{u^{2} \cos^{2} ϕ}{2 g}$

From $ϕ = 0 to ϕ = 90$

$h_{m}$ decreases with $\cos^{2}$ function.

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