Imagine dropping a steel ball bearing into a tall cylinder full of motor oil, Viscous drag has a significant effect on the ball bearing's downward velocity, 11(t). One family of dynamic models for this takes the form d1: (*) R-gikvpt 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 (9;) is the familiar frictionfree approximation for a falling mass. The exponentp is an interesting topic for dicussion: for this problem we considerp : 1. In this problem, we use SI units, so if is in seconds,v is in metres per second, etc. Use the international standard value 9 = 9.807 and assume motor oil has viscosity parameter k : 2L5. (a) Find vhf), (Assume 11(0) = 0.) v(t) = (9.807e/'(21.5t)e"(logQ.807))/21 .5 (b) Let y(t) denote the distance the ball bearing has dropped attime t. [This terminology entails y(0) : 0, and y(t) > Ofort > 0.) Find y(t). W) = (Is) 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 =