In Jules Verne\'s classic novel, From the Earth to the Moon, a giant cannon dug

Question

In Jules Verne's classic novel, From the Earth to the Moon, a giant cannon dug into the Earth in Florida fired a spacecraft all the way to the Moon. (a) If the spacecraft leaves the cannon at escape speed, at what speed is it moving when 1.40 105 km from the center of the Earth? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s

Explanation / Answer

the difference in potential energy between the surface and the location given is equal to the loss of kinetic energy starting from escape velocity of 1.1187 * 104 m/s: GMm(1/6.371 * 106 m - 1/1.40 * 108 m) = (0.5m)((1.1187 * 104 m/s)2 - vf2) (2)(6.6738 * 10-11 m3/kg s2)(5.9736 * 1024 kg)(1.498 * 10-7 m-1) = 1.2515 * 108 m2/s2 - vf2 1.1945 * 108 m2/s2 = 1.2515 * 108 m2/s2 - vf2 vf = 2386 m/s (b) t = v/a and d = at2/2 = (v/a)2(a/2) = v2/2a so a = v2/2d = (1.1187 * 104 m/s)2/(2 * 1.73 * 103 m) = 3.62 * 104 m/s2

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