Question

An alien observer passes the earth at 0.60c 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?

a. 59.6 m
b. 73.1 m
c. 74.6 m
d. 91.4 m
e. 114 m

Answer 1

When an object is moving at a significant fraction of the speed of light, its length appears shorter to an observer in a stationary frame of reference. In this case, the length of the field as observed by the alien traveling at 0.60c is approximately 74.6 meters. Option number C is correct.

Step-by-step explanation:

When an object is moving at a significant fraction of the speed of light, its length appears shorter to an observer in a stationary frame of reference. This phenomenon is known as length contraction.

In this case, the alien observer is traveling at 0.60c relative to the earth. According to length contraction, the length of the field will appear shorter to the alien observer.

To calculate the length as observed by the alien, we can use the formula for length contraction: L' = L / √(1 - v²/c²), where L is the length of the field in the earth's frame of reference, v is the velocity of the observer, and c is the speed of light.

Plugging in the values, the length of the field as observed by the alien observer is approximately 74.6 meters.