An aerplane travels over a rectangular field `100 m xx 50m` parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame?

Explanation

The rectangular field appears to be a square when the length becomes equal to the breadth (i.e. 50 m.)
(i.e. L' = 50 = L = 100, v = ? `
`Velocity of light
` c = 3 xx 10^(8)m/s`
We know ` L' = L (sqrt 1 - v^(2)c^(2))`
` rArr 50 = 100 (sqrt 1 - v^(2) / c^(2) ) `
`rArr (1 / 2)^(2) = 1 - v^(2) / c^(2)`
` rArr 1/ 4 = v^(2) / c^(2) `
`rArr 1 / 4 = c^(2) - v^(2) / c^(2) `
`rArr c^(2) / 4 = c^(2) - v^(2)
` rArr v^(2) = c^(2) - c^(2) / 4`
` rArr 3 c^(2) / 4 `
` rArr v = (sqrt 3c) / 2 = 0.866 C`