An object falling vertically through the air is subjected to viscous resistance as well...

An object falling vertically through the air is subjected to viscous resistance as well as to the force of gravity. Assume that an object with mass m is dropped from a height s0 and that the height of the object after t seconds is

where g = 32.17 ft/s² and k represents the coefficient of air resistance in lb-s/ft. Suppose s₀ = 300 ft, m = 0.25 lb, and k = 0.1 lb-s/ft. Find, to within 0.01 s, the time it takes this quarter-pounder to hit the ground.