Problem

A person wearing a jet pack lifts off from rest and ascends along a straight vertical traj...

A person wearing a jet pack lifts off from rest and ascends along a straight vertical trajectory. Let M denote the initial combined mass of the pilot and the equipment, including the fuel in the pack. Assume that the mass flow rate mo and exhaust gas speed υo are known constants and that the pilot can take off as soon as the rocket engine is started. If the exhaust engine is completely directed in the direction of gravity, determine the expression of the pilot’s speed as a function of time, M, mo, υo, and g (the acceleration due to gravity) while the pack is providing a thrust. Neglect air resistance and assume that gravity is constant.