1. A 20-kg child swings back and forth on a swing such that her height h in m from the ground as a function of x is described by: h(x) = 0.5 + 0.45x2 for -1.2 m ? x ? 1.2 m
(a) What is the position of the child when x = 0?
(b) Show graphically how the potential and kinetic energies of the child vary with x.
(c) What is the maximum potential energy of the child?
(d) At what point does the child have maximum speed?
(e) Use the law of conservation of energy to calculate the maximum speed of the child.