Question

A spaceship passes you at a speed of 0.90c. You find the length of the ship in your frame of reference to be 50.0 m. A few months later, the ship docks, and you measure its length with a tape measure. What length does the tape measure show?

Answer 1

According to the theory of relativity, the length of an object appears to contract when observed from a different frame of reference at high velocities. The observed length of the spaceship would be approximately 22.0 m.

Step-by-step explanation:

According to the theory of relativity, when an object moves at a high velocity, its length appears to contract in the direction of motion when observed from a different frame of reference. This phenomenon is known as length contraction.

The equation that relates the observed length of the spaceship to its proper length is:

L = Lo √(1 - v^2/c^2)

where L is the observed length, Lo is the proper length, v is the velocity of the spaceship, and c is the speed of light.

Given the proper length of the spaceship as 50.0 m and the velocity as 0.90c, we can calculate the observed length using the above equation.

L = 50.0 m √(1 - (0.90c)^2/c^2)

Using the Lorentz factor (√(1 - (0.90c)^2/c^2) ≈ 0.44, the observed length is approximately 22.0 m.