10.Question 10Imagine that you are traveling in a spaceship that passes by Earth at a velocity of 0.87c (Lorentz factor = 2), and you fire an escape pod from your spaceship pointed straight up (in the y or z direction, perpendicular to the spaceship’s direction of travel). If the escape pod has a perpendicular speed of 0.6c with respect to your ship, what is the perpendicular speed of the escape pod from the perspective of a person on Earth?
Question
10.Question 10Imagine that you are traveling in a spaceship that passes by Earth at a velocity of 0.87c (Lorentz factor = 2), and you fire an escape pod from your spaceship pointed straight up (in the y or z direction, perpendicular to the spaceship’s direction of travel). If the escape pod has a perpendicular speed of 0.6c with respect to your ship, what is the perpendicular speed of the escape pod from the perspective of a person on Earth?
Solution
To solve this problem, we need to use the relativistic velocity addition formula, which is:
V = (v1 + v2) / (1 + (v1*v2/c^2))
where:
- V is the total velocity,
- v1 is the velocity of the spaceship relative to Earth (0.87c),
- v2 is the velocity of the escape pod relative to the spaceship (0.6c),
- c is the speed of light.
Substituting the given values into the formula, we get:
V = (0.87c + 0.6c) / (1 + (0.87c * 0.6c / c^2))
Solving the equation, we get:
V = 1.47c / (1 + 0.522)
V = 1.47c / 1.522
V = 0.966c
So, the perpendicular speed of the escape pod from the perspective of a person on Earth is approximately 0.966 times the speed of light.
Similar Questions
8.Question 8If you are traveling in a spaceship that passes by Earth at a velocity of 0.8c, and you fire an escape pod from your spaceship (pointed in your direction of travel) that has a speed of 0.7c with respect to your ship, what is the speed of the escape pod from the perspective of a person on Earth? (Note: You don’t need a calculator to answer this question--think about the possible answers listed.)1 point0.7c0.8c1.5cNone of the above
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