A projectile is fired with velocity u making angle θ with the horizontal. What is the angular momentum of the projectile at the highest point about the starting point ? Given that mass of the projectile is m

Maximum height, $\mathrm{h}=\frac{{\mathrm{u}}^2{\sin }^2\mathrm{\theta }}{2\mathrm{g}}$

Linear momentum at highest point $=\mathrm{mucos}\mathrm{\theta }$

Angular momentum of the projectile at the highest point

$=\text{ linear momentum }\times \text{ perpendicular distance }$

$\begin{array}{l}=\mathrm{mucos}\mathrm{\theta }\times \mathrm{h}=\mathrm{mucos}\mathrm{\theta }\times \left({\mathrm{u}}^2{\sin }^2\mathrm{\theta }/2\mathrm{g}\right)\\ =\frac{{\mathrm{mu}}^3{\sin }^2\mathrm{\theta cos}\mathrm{\theta }}{2\mathrm{g}}\end{array}$