3 Dudley is dropped out of a plane and falls vertically toward the earth Dudley s acceleration is the sum of two components a downward acceleration due to gravity equal to g 9 8 kg m s an acceleration in the opposite direction to Dudley s current velocity and proportional to this velocity a Write a differential equation that describes Dudley s vertical velocity as a function of time Choose downward as the positive direction There will be an as yet undetermined constant of proportionality involved call it k b Compute an explicit formula for Dudley s velocity as a function of time assuming that i Dudley will approach a maximum vertical speed of 65 m s and ii that Dudley is shoved out of the plane with an initial downward velocity of 5 m s