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An electron is moving in the positive x-direction, in S' frame. The relative velocity between the S and S' frames is 0.7C and the velocity of the electron is also 0.7C with respect to an observer in S' frame. The velocity of the electron for an observer in the S frame (in term of C) is _____.
Correct answer is '0.94'. Can you explain this answer?
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An electron is moving in the positive x-direction, in S' frame. Th...
The relative relativistic velocity is given as
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An electron is moving in the positive x-direction, in S' frame. Th...
Given information:
- The relative velocity between the S and S' frames is 0.7C.
- The velocity of the electron with respect to an observer in the S frame is also 0.7C.
Explanation:
To solve this problem, we need to use the relativistic velocity addition formula. The formula is given by:
v' = (v + u) / (1 + (vu/c^2))
Where:
- v' is the velocity of the electron as observed in the S' frame.
- v is the velocity of the electron as observed in the S frame.
- u is the relative velocity between the S and S' frames.
- c is the speed of light in a vacuum.
Step 1: Convert the velocities into appropriate units
- We are given that the relative velocity u = 0.7C.
- The velocity v of the electron is also given as 0.7C.
Step 2: Apply the velocity addition formula
- Plugging the values into the formula, we have:
v' = (0.7C + 0.7C) / (1 + (0.7C * 0.7C / C^2))
Simplifying the equation:
v' = 1.4C / (1 + 0.49)
v' = 1.4C / 1.49
Step 3: Calculate the velocity as observed in the S' frame
- Dividing the numerator by the denominator:
v' = 0.94C
Therefore, the velocity of the electron as observed in the S' frame is 0.94C.
Conclusion:
The correct answer is 0.94C. This result implies that the electron appears to be moving at a speed of 0.94 times the speed of light as observed from the S' frame.
- The relative velocity between the S and S' frames is 0.7C.
- The velocity of the electron with respect to an observer in the S frame is also 0.7C.
Explanation:
To solve this problem, we need to use the relativistic velocity addition formula. The formula is given by:
v' = (v + u) / (1 + (vu/c^2))
Where:
- v' is the velocity of the electron as observed in the S' frame.
- v is the velocity of the electron as observed in the S frame.
- u is the relative velocity between the S and S' frames.
- c is the speed of light in a vacuum.
Step 1: Convert the velocities into appropriate units
- We are given that the relative velocity u = 0.7C.
- The velocity v of the electron is also given as 0.7C.
Step 2: Apply the velocity addition formula
- Plugging the values into the formula, we have:
v' = (0.7C + 0.7C) / (1 + (0.7C * 0.7C / C^2))
Simplifying the equation:
v' = 1.4C / (1 + 0.49)
v' = 1.4C / 1.49
Step 3: Calculate the velocity as observed in the S' frame
- Dividing the numerator by the denominator:
v' = 0.94C
Therefore, the velocity of the electron as observed in the S' frame is 0.94C.
Conclusion:
The correct answer is 0.94C. This result implies that the electron appears to be moving at a speed of 0.94 times the speed of light as observed from the S' frame.
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An electron is moving in the positive x-direction, in S' frame. The relative velocity between the S and S' frames is 0.7C and the velocity of the electron is also 0.7C with respect to an observer in S' frame. The velocity of the electron for an observer in the S frame (in term of C) is_____.Correct answer is '0.94'. Can you explain this answer?
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