Two small disks A and B of mass 3 kg and 1.5 kg, respectively, may slide on a horizontal, frictionless surface. They are connected by a cord, 600 mm long, and spin counterclockwise about their mass center G at the rate of 10 rad/s. At t = 0, the coordinates of G are x0¯¯¯¯¯=0, y0¯¯¯¯¯=2m, and its velocity v¯¯¯0=(1.2m/s)i+(0.96m/s)j. Shortly thereafter the cord breaks; disk A is then observed to move along a path parallel to the y axis, and disk B moves along a path that intersects the x axis at a distance b = 7.5 m from O. Determine
(a) the velocities of A and Bafter the cord breaks,
(b) the distance a from the y axis to the path of A.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?