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FIG. 1: Diagram for Prob 3 2) A rocket is launched vertically up from the ground. Assume that the gravita- tional acceleration of the Earth is uniform, g = 9.8 ms 2. The rocket ejects fuel at an exponential rate, m = moe-kt, and the total time it takes to exhaust all the available fuel is T. The exhaust speed vex is constant. Find the maximum altitude, Zmax, that the rocket can reach. [Answer: Zmax kvext? (kvex – 9).] 29 = 3) A uniform solid bar of length l is standing vertically on a frictionless surface (think of a very slippery ice). At the time t 0 the bar is slightly disturbed so that it starts falling down on the surface (the disturbing force does not matter as long as it is very small). Find the trajectory of the upper end of the bar, x(t) and y(t) (the choice of coordinate system is shown in Figure 1). C 2 INT A+ X FIG. 1: Diagram for Prob 3

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