Unusual Faster-Than-Speed-of-Light Situation

Classical Mechanics Level 4

A physics student attaches a laser pen to an ultra-fast robotic arm, pointing it at the moon. Consider a spherical moon, in which the laser is visible as a dot. A single rapid flick of the arm moves the dot from point \( A \) to point \( B \) in a 120 degree arc through the lunar surface. Calculate the maximum interval of time \( \Delta t_{\text{max}} \), in milliseconds, in which the movement of the arm could take place so that the laser dot moves twice as fast as the speed of light \( c \) in the lunar surface.

Details and assumptions

  1. Lunar radius is \( = 1737.1 \text{ km} \).
  2. Speed of light is \( c = 3 \times 10^{5} \text{ km/s} \).
  3. Take \( \pi = 3.14 \).
  4. The result is a single digit integer

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