Physics

Problem

A pilot wearing a jet-pack of negligible mass stands on a balcony. The combined mass of the pilot and remaining fuel is

80\,\text{kg}

. The jet ejects air vertically downward at a constant mass flow rate of

2\,\text{kg\,s}^{-1}

with an exhaust speed of

30\,\text{m\,s}^{-1}

relative to the pack. Answer the following questions. a. (i) Derive an expression for the magnitude of the upward thrust produced by the jet in terms of the mass flow rate

\dot m

and the exhaust speed

v_e

. b. (ii) Using the given values, calculate the initial vertical acceleration of the pilot just as the jet is switched on. Take

g = 9.8\,\text{m\,s}^{-2}

. c. (iii) Discuss qualitatively how the acceleration would change if the pilot continues to burn fuel so that the total mass gradually decreases while

\dot m

and

v_e

remain the same.

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