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 x 105km 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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