Consider a universe in which the speed of light c is equal to 100 mi/h. A lincoln continental traveling at a speed v relative to a fixed radar speed trap overtakes a Volkswagen traveling at the speed limit of 50 mi/h. The lincoln's speed is such that its length, as measured by the fixed observer, is the same as that of the Volkswagen. By how much is the Lincoln exceeding the speed limit? At rest, a Lincoln is twice as long as a Volkswagen.
Length contraction L = gamma Lo
The Attempt at a Solution
I set L = .5 Lo which makes gamma = 2, solving that gives me v = .866c and that the Lincoln is speeding by 36.6 mi/h. The answer in the back of the book is 40 mi/h. Did I do something wrong, or is it just a significant figure difference?