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An airplane of rest length 40.0 m is moving uniformly with respect to earth, at a speed of 630 m/s.By what fraction of is rest length it is shortened for the observer on earth?
The length contraction formula is L = L0/γ where L0 is the proper length (measured in the reference frame of the object) and γ = 1/√(1-β^2) with β= v/c. You have v = 590m/s so β=v/c = 0.0000019666... That gives you a value of γ = 1.000000000001933888 The length is shortened by L0-L, so the fraction it is shortened is (L0-L)/L0 = 1-L/L0 = 1-1/γ = 0.000000000001933888
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