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 wholetime of motion of the body, and the instantaneous power of gravity as a function of time.

Explanation

The velocity of the body, t seconds after the beginning of the motion becomes `vecv=vecv_0+vec(g t)`. The power developed by the gravity `(mvecg)` at that moment, is
`P=mvecg*vecv=m(vecg*vecv_0+g^2t)=mg(g t-v_0sin alpha)` (1)
As `mvecg` is a constant force, so the average power
`lt P geA/tau=(mvecg*Deltavecr)/(tau)`
where `Deltavecr` is the net displacement of the body during time of flight.
`mvecg_|_Deltavecr` so `lt P gt = 0`