Please see the attached file.
The basic assumptions behind the Theory of Relativity are that the speed of light in a vacuum is a universal constant and that all motion and perception is relative. These in turn affect how we perceive things moving relative to us. Using the Relativity simulation, investigate these phenomena. Follow the instructions below and then answer the questions at the bottom of this sheet.
2. You are traveling at 99% the speed of light. As you approach a meter stick, what would you perceive its length (in centimeters) to be?
3. You observe a spaceship coming towards you at a high rate of speed. A clock on board the spaceship appears to be running about 2.5 times slower than your clock. How fast is the spaceship going relative to you?
4. What value would you measure for the speed of the light (in miles/second) coming from the moving object in question 3?
(1) Apparent mass M = m/sqrt[1 - (v/c)^2]
M = 2m = m/sqrt[1 - (v/c)^2]
sqrt[1 - (v/c)^2] = 1/2
1 - (v/c)^2 = 1/4
(v/c)^2 = 1 - 1/4 = 3/4
v/c = sqrt(3/4) = ...
The file contains solutions to all the four questions.