Question

an alien observer passes the earth at 0.600c and measures the length of an american football field while traveling in the direction from one end zone to the other end zone. on the field, the distance from end zone to end zone is 91.4 m. how long does the field appear to be according to the alien observer?

Answer 1

The field appears to be approximately 73.12 meters long according to the alien observer.

Step-by-step explanation:

The length contraction formula, used in special relativity, can be used to calculate how lengths appear to change when an object is moving at relativistic speeds. According to this formula, the length of an object in the direction of motion decreases as its speed increases.

In this case, the alien observer is traveling at 0.600c (where c is the speed of light) relative to Earth. To find the length of the field as it appears to the alien observer, we can use the length contraction formula:

L' = L * sqrt(1 - (v^2/c^2))

Plugging in the given values:

L' = 91.4 m * sqrt(1 - (0.600c)^2/(c^2))

L' = 91.4 m * sqrt(1 - 0.360)

L' = 91.4 m * sqrt(0.640)

L' = 91.4 m * 0.8

L' = 73.12 m

Therefore, the field appears to be approximately 73.12 meters long according to the alien observer.