Question

An astronaut on a spaceship traveling at a speed of 0.635c is holding a meter stick (length of 1m) parallel to the direction of motion. There are two observers (La​ and LB) on earth separated by a distance of 2m, each of them measures the stick as it passes. How do the three measurements of length compare?

Answer 1

The length of the stick appears shorter for the observers on Earth due to length contraction.

Step-by-step explanation:

The length of an object can be different for observers moving relative to each other due to a phenomenon known as length contraction. In this case, the astronaut on the spaceship measures the length of the meter stick to be 1m. However, for the observers on Earth, the length of the stick appears shorter. This is because, according to the theory of relativity, the length of an object appears contracted for observers in a different frame of reference who are moving relative to the object.

The observer on Earth measures the length of the stick to be shorter due to the effect of length contraction. The amount of contraction can be calculated using the formula for length contraction:

L' = (1 / γ)L

where L' is the measured length, L is the proper length (length in the frame of the stick), and γ is the Lorentz factor which depends on the relative velocity between the observer and the object.