An aeroplane flies over a rectangular field of dimensions 100 m 50 m , moving parallel to its length. Determine the speed of the plane such that the field appears as a square in the plane's frame of reference.

Step-by-step solution

Let the proper length of the field be L₀ = 100 m and the proper width be W₀ = 50 m . The aeroplane moves parallel to the length of the field with speed v . According to the theory of relativity, the length of the field observed from the aeroplane undergoes length contraction, while the width remains unchanged. The observed length is given by L = L₀ 1 - v^2 c^2 . The observed width is W = W₀ = 50 m . For the field to appear as a square in the aeroplane's frame of reference, the observed length must be equal to the o