A body falling vertically under gravity encounters resistance of the atmosphere. If the resistance varies as the velocity, show that the equation of motion is given by du g-ku dt where u is the velocity, k is a constant and g is the acceleration due to gravity. Show that as dx t increases, u approaches the value g/k. Also, if u = where x is the distance fallen by the body from rest in time t, show that dt X= gt 8 4- (1-e) k