1) Let's continue to investigate your space vacation from last week. Your spaceship, which has a proper length of 300 m, passes near a space platform while you are moving at a relative speed of 86% the speed of light (so v=0.86*c). What is the length of the spaceship when measured by someone on the space platform?
Equation for length contraction
L = L' * √ (1 - v2/c2)
Where:
L = The length of the spaceship as seen by the observer
L' = The proper length of the spaceship
v = The velocity of the spaceship
c = The speed of light.
You have already answered the question. Use the length contraction formula.
L = L' * �ã (1 - v^2/c^2)
= L'* sqrt(0.2604)
= 0.51 L'
To find the length of the spaceship when measured by someone on the space platform, we can use the equation for length contraction:
L = L' * √(1 - v^2/c^2)
In this equation, L represents the length of the spaceship as seen by the observer on the space platform, L' represents the proper length of the spaceship, v represents the velocity of the spaceship, and c represents the speed of light.
Given that the proper length of the spaceship (L') is 300 m and the relative speed of the spaceship (v) is 0.86 times the speed of light (c), we can substitute these values into the equation:
L = 300 * √(1 - (0.86)^2/(1^2))
Simplifying further:
L = 300 * √(1 - 0.7396)
L = 300 * √0.2604
L ≈ 300 * 0.5102
L ≈ 153.06 m
Therefore, the length of the spaceship, as measured by someone on the space platform, is approximately 153.06 meters.