Question

A spaceship, 195 m long as seen on board, moves by the Earth at 0.815c. What is its length as measured by an Earth-bound observer?

Answer 1

Length contraction occurs in special relativity when an object is moving at a high velocity relative to an observer. The length of the spaceship as measured by an Earth-bound observer can be calculated using the Lorentz transformation formula. The length of the spaceship, as measured by an Earth-bound observer, is approximately 108.62 meters.

Step-by-step explanation:

In special relativity, length contraction occurs when an object is moving at a high velocity relative to an observer. According to the Lorentz transformation, the length of the spaceship as measured by an Earth-bound observer can be calculated using the formula:

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

where L' is the length as measured by the Earth-bound observer, L is the length as seen on board the spaceship, v is the velocity of the spaceship, and c is the speed of light in a vacuum.

Using the given values, we can substitute them into the formula to find the length:

L' = 195 m * sqrt(1 - (0.815c)^2 / c^2)

Calculating this, we find that the length of the spaceship as measured by an Earth-bound observer is approximately 108.62 meters.