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A body of mass $m$ is thrown with velocity u from the origin of a co-ordinate axes at an angle $\theta$ with the horizon. The magnitude of the angular momentum of the particle about the origin at time $\mathrm{t}$ when it is at the maximum height of the trajectory is proportional to
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$\mathrm{u}^3$
$\vec{L}=m u \cos \theta h_{\max }=m u \cos \theta \frac{u^2 \sin ^2 \theta}{2 g} \Rightarrow L=\frac{m u^3 \sin ^2 \theta \cos \theta}{2 g} \quad L \propto u^3$
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