A pilot wearing a jet-pack of negligible mass stands on a balcony. The combined mass of the pilot and remaining fuel is 80kg. The jet ejects air vertically downward at a constant mass flow rate of 2kgs−1 with an exhaust speed of 30ms−1 relative to the pack.
Answer the following questions.
(i) Derive an expression for the magnitude of the upward thrust produced by the jet in terms of the mass flow rate m˙ and the exhaust speed ve.
(ii) Using the given values, calculate the initial vertical acceleration of the pilot just as the jet is switched on. Take g=9.8ms−2.
(iii) Discuss qualitatively how the acceleration would change if the pilot continues to burn fuel so that the total mass gradually decreases while m˙ and ve remain the same.