An alien spacecraft flies directly over a football stadium at a speed of 0.50c. If the proper length of the field is 100 yards, what field length is measured by the crew of the alien spacecraft?

Question

Quizplus · Accepted Answer

We can use the Lorentz contraction formula to find the length of the football field measured by the crew of the alien spacecraft.

L' = L√(1 - v^2/c^2)

Where L is the proper length of the football field, v is the velocity of the spacecraft (0.50c), c is the speed of light, and L' is the length measured by the crew of the spacecraft.

Plugging in the numbers:

L' = 100 yards * √(1 - (0.50c)^2/c^2)
L' = 100 yards * √(1 - 0.25)
L' = 100 yards * √0.75
L' = 100 yards * 0.866
L' = 86.6 yards

So the field length measured by the crew of the alien spacecraft is approximately 87 yards, which is answer choice C.

An Alien Spacecraft Flies Directly Over a Football Stadium at a Speed