A tourist walking at a speed of 1.5 m/s along a 7.5 km path that follows an old canal. If the speed of light in a vacuum were 3.0 m/s, how long would the path be, according to the tourist?
2007-03-17 05:01:49 · 2 answers · asked by marinatedpickles 2 in Science & Mathematics ➔ Physics
If the speed of light in a vacuum was 3 m/s, the traveler would be going at half the speed of light. This would cause gamma to become 2/sqrt(3). Gamma is the factor by which the length differs according to the two observers. The traveler would then see the length as:
L = Lo / gamma
L = 7.5/(2/sqrt(3))
L = 6.5 meters
If you're wondering how to find gamma, its:
gamma = (1 - (v/c)^2)^(-1/2)
where c is the speed of light.
2007-03-17 05:13:04 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The path would still be 7.5 km long, as the tourist would discover by taking 5,000 seconds to walk it, but it would appear to be 6.495 km long. Now the question is, "Does the tourist believe that he is walking at 1.299 m/s or that the trip takes 5,774 seconds, or both?"
2007-03-17 07:49:08 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋