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Solutions to Exercise 22
(a) The vehicle has mass m = 1000 kg. The observer sees the vehicle with a mass m' = m / sqrt(1 - (v/c)^2) = 1000 / sqrt(1 - (0.5c/c)^2) = 1000 / sqrt(0.75) = 1000 kg / 0.866 = 1150 kg. (b) for v = 0.7 * c, m' = 1000 / sqrt(1 - (0.7c/c)^2) = 1000 / sqrt(0.51) = 1400 kg. (c) for v = 0.999995 * c, m' = 1000 / sqrt(1 - (0.999995c/c)^2) = 1000 / sqrt(0.000009999975) = 1000 / 0.00316 = 316000 kg. |