Relativity (lorentz contraction)

AI Thread Summary
The discussion focuses on calculating the length contraction of a spacecraft runway as observed by a pilot flying at a high speed relative to Earth. The initial length of the runway is given as 3.6 km, and the pilot's speed is 4.00 x 10^7 m/s. The user applied the length contraction formula, resulting in a calculated length of 3351 m. There is confusion regarding the correct application of the Lorentz factor, particularly whether the speed should be squared in the calculation. Clarification is sought on whether the approach taken is correct or if there is a misunderstanding of the variables involved.
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Homework Statement


As measured by an observer on earth, a spacecraft runway has a length of 3.6km. What is the length of the runway as measured by the pilot of a spacecraft flying directly over the runway at a speed 4.00 x10^7 m/s relative to the earth?

Homework Equations


L= Lnot/γ

The Attempt at a Solution


I inserted 3.6km as the Lnot and got 3351m as the answer by using the equation.
L= 3600/ (1/sqrt(1-4.0E7/3.0E8))
= 3351m
Is this true? Or i have confused the L as Lnot? I got the answer as i figure the pilot is in rest and the runway is moving relative to him.
 
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