An object of mass ' $m$ ' is projected with an initial velocity ' $u$ ' with an angle of ' $\theta$ ' with…
An object of mass ' $m$ ' is projected with an initial velocity ' $u$ ' with an angle of ' $\theta$ ' with the horizontal. The average power delivered by gravity in reaching the highest point.
$\frac{\mathrm{mgu} \sin ^2 \theta}{2}$
$\frac{m u^2 \sin ^2 \theta}{2 g}$
$\frac{m g \sin \theta}{2 u}$
$\frac{\mathrm{mgu} \sin \theta}{2}$
Solution
At highest point of the projectile,
$\begin{aligned}
& \mathrm{P}_{\mathrm{av}}=\frac{\mathrm{W}_{\mathrm{g}}}{\frac{\mathrm{~T}}{2}}=\frac{2 \mathrm{mg} \mathrm{H}_{\max }}{\mathrm{T}}=\frac{2 \mathrm{mg}\left(\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}}\right)}{\left(\frac{2 \mathrm{u} \sin \theta}{\mathrm{~g}}\right)} \\
& =\frac{1}{2} \mathrm{mgu} \mathrm{\sin } \mathrm{\theta}
\end{aligned}$