Question

5.168 The Earth has a radius of approxinh ever 6000 km and rotates around its axis every 24 h. James begins at the South Pole and flies, drives, and boats so that he is always going due North at 50 km/h. (Note that he maintains a distance of 6000 km from the center of the Earth-the origin-and that while he trav- els North, he is also spinning with the Earth.) We take the axis of rotation as our z-axis. (a) How long does it take James to travel from (b) Give the spherical functions r(t), θ(t), (c) Give the cylindrical functions p(t), φ(t), z(t) the South Pole to the North Pole? φ(t) that represe ntJames' motion. that represent his motion. (Your answers will be easier to interpret if you simplify them with a few trig identities.) (d) At what time does James reach the equator? Explain how you can tell that your ρ and z functions make sense at this time. (e) At what time does James reach the North Pole? Explain how you can tell that your ρ and z functions make sense at this time. (f) Give the Cartesian functions x(), y(0), 2(t) that represent his motion.

Answer 1

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