Mysterious airplane
Classical Mechanics
Level
1
When an airplane flies far up in the sky, it appears to be very small and we can cover it with our hand.
What happens to the size of the plane?
It is just an optical illusion as it stays the same size
The airplane shrinks as it flies higher
According to the theory of relativity, the length contracts as it flies faster
According to the theory of gravity, the expands as it gets further from the Earth
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1 solution
The size of the airplane does not change, but it appears smaller. It is an optical illusion. For the eye, magnification is directly proportional to angle subtended at the eye, by the object. As the object moves far off from the eyes, the angle subtended decreases, therefore, the object appears smaller in size.
Also, it is true that according to the theory of relativity, the length of objects decreases with increase in speed. But, this phenomenon of length contraction is noticeable at very high speeds (speeds close to the speed of light). The airplane flies typically at 8 0 0 km/h to 1 0 0 0 km/h , which is far less than the speed of light ( 1 . 0 8 × 1 0 9 km/h ).