Question

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?

Answer 1

In the context of Special Relativity, an alien spacecraft travelling at half the speed of light would observe the length of a 100-yard football field to contract to approximately 79.39 meters due to length contraction.

Step-by-step explanation:

The question involves the concept of length contraction, a phenomenon from Einstein's theory of Special Relativity, observed when an object moves at a significant fraction of the speed of light (denoted as c). When the alien spacecraft flies over the football stadium at a speed of 0.50c, the proper length of the football field (100 yards) as measured by the crew of the spaceship will appear contracted.

The length contraction formula is
`L = L_0 / √( 1 - v^2/c^2),` where L is the observed contracted length, L_0 is the proper length, and v is the relative velocity of the length as measured in the stationary frame. To convert 100 yards to meters, we use the conversion that 1 yard = 0.9144 meters, thus 100 yards = 91.44 meters. Applying the length contraction formula, the measured field length L by the crew of the spacecraft would be L =
`91.44 / √(1 - (0.50c)^2/c^2)`, which calculates to approximately L = 79.39 meters.

Answer 2

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