Solve conversation of energy problem involving gravitational potential energy?

While she is being lifted, and while she is going down she is moving so must have kinetic energy. By tradition we define the ground to be at zero potential energy. there is no particular reason for this other than that it is convenient for calculation. If that is the case her minimum Potential energy is zero when she is on the ground. Her maximum potentlial energy ( E= mgh) is at the highest point from the ground. m = 9 Kg , g= 9.8 m/s^2 h = 1.5 m so E = 9 * 9.8 * 1.5 = 132 J

P.E. = mgh so P.E. can arbitrarily be assigned 0 on the floor, then P.E. = 9kg*9.8*1.5 = 132.3 J = max P.E. You can't give a K.E. because that depends on how fast he lifts the child. If he lifts his child with velocity v then of course K.E. = 1/2 m v^2. v does not have to be constant. But suppose he lifts the child with constant power P. Then P = (dW/dt ) = (dW/dh)*(dh/dt) = v*dW/dh = mgv where W = work done as a function of h = mgh. Then v = P/mg and K.E. in that case is a constant 1/2 m (P/mg)^2 = P^2/(2mg^2).

her maximum potential energy will be at max height as the P.E is the energy possesed by the virtue of position from ground and the minimum will be on ground

P.E. = mgh so P.E. can arbitrarily be assigned 0 on the floor, then P.E. = 9kg*9.8*1.5 = 132.3 J = max P.E. You can't give a K.E. because that depends on how fast he lifts the child. If he lifts his child with velocity v then of course K.E. = 1/2 m v^2. v does not have to be constant. But suppose he lifts the child with constant power P. Then P = (dW/dt ) = (dW/dh)*(dh/dt) = v*dW/dh = mgv where W = work done as a function of h = mgh. Then v = P/mg and K.E. in that case is a constant 1/2 m (P/mg)^2 = P^2/(2mg^2).

her maximum potential energy will be at max height as the P.E is the energy possesed by the virtue of position from ground and the minimum will be on ground