Question

A body of mass $m$ is thrown at an angle $\alpha$ to the horizontal with the initial velocity $v_0$. Find the mean power developed by gravity over the whole time of motion of the body, and the instantaneous power of gravity as a function of time.

Answer 1

The velocity of the body $t$ sec. after the beginning of the motion becomes

$\overline{V}=\overline{u}+\overline{gt}$

The power developed by the gravity $\overline{mg}$ at that moment is

$P_{ins}=\overline{mg}.\overline{v}=m(\overline{g}.\overline{V_0}+g^{2}t)$

$=mg(gt-v_{0}sin\alpha )$

As $\overline{mg}$ is a constant force, so the e\average power,

$p_{av}=\frac{A}{T}=\frac{\overline{mg}.\Delta \overline{r}}{T}$

where $\Delta \overline{r}$is the net displacement of the body during time of the flight

as $\overline{mg}\perp \Delta \overline{r}$

so $p_{av}=0$