Imagine dropping a steel ball bearing into a tall cylinder full of glycerine. Viscous drag has a significant effect on the ball bearing's downward velocity, v(t). One family of dynamic models for this takes the form (it) 7 : 7 'P (*) d, g M , where g is the acceleration of gravity and k is a constant. The size of k is related to the viscosity of the medium: when k: : 0, equation (*) is the familiar friction- free approximation for a falling mass. The exponentp is an interesting topic for dicussion: for this problem we consider p : 1. In this problem, we use SI units, so t is in seconds, 1) is in metres per second, etc. Use the international standard value 9 : 9.807 and assume glycerine has Viscosity parameter k : 23. (a) Find 11(t). (Assume 0(0) : 0.) \"(19) : (b) Let y(t) denote the distance the ball bearing has dropped at time t. (This terminology entails y(0) = O, and y(t) > 0 fort > 0.) Find y(t). ya) : (c) Using computer assistance as appropriate, find the time required for the ball bearing to drop 1 metre from its release point. y(t) : 1 when t =