A body is thrown with a velocity v_(0) at an angle theta_(0) with horizontal. Find the (i) instan-taneous power delivered by gravity after a time t measured from the instant of projection (ii) average power delivered by gravity during the time t.

A body is thrown with a velocity v_(0) at an angle theta_(0) with hori

1.	A body is thrown with a velocity v_(0) at an angle theta_(0) with horizontal. Find the (i) instan-taneous power delivered by gravity after a time t measured from the instant of projection (ii) average power delivered by gravity during the time t.
Answer» Solution :(i) Power : Power DELIVERED by gravity after a time t when the PARTICLE has velocity v is, `P_(g) = m vec(g).vec(v)""...(i)` Kinematics : Substituting `vec(g) = - g vec(j) and vec(v) = v_(0) cos theta_(0) hat(i) + (v_(0) SIN theta_(0) - "gt")`j in eq. (i), We have `P_(g) = - mg (v_(0) sin theta_(0) - "gt")` (ii) The average power is `P_(av) = (int_(0)^(t) PDT)/(t)` Substituting `P = - mg (v_(0) sin theta_(0) -"gt")`, we have `P_(av) = - (mg)/(t) int_(0)^(t) (v_(0) sin theta_(0) -"gt")dt` This gives `P_(av) = - mg(v_(0) sin theta_(0) - ("gt")/(2))` Note : If t = T (time of light), then `P_(av)` = zero