A rock of mass 12 kg is tied to a string of length 2.4 m, with the other end of the stri...

A rock of mass 12 kg is tied to a string of length 2.4 m, with the other end of the string fastened to the ceiling of a tall room (Fig. P6.42). While hanging vertically, the rock is given an initial horizontal velocity of 2.5 m/s. (a) Add a coordinate system to the sketch in Figure P6.42. Where is a convenient place to choose the origin of the vertical (y) axis? (b) What are the initial kinetic and potential energies of the rock? (c) If the rock swings to a height h above its initial point, what is its potential energy? What is its total mechanical energy at that point? (d) How high will the rock swing? Express your answer in terms of the angle that the string makes with the vertical when the rock is at its highest point. (e) Make qualitative sketches of the kinetic energy and potential energies as functions of height h.