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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 0.8 c and the velocity of the electron is also 0. 8 c with respect to an observer in S frame. The velocity of the electron for an observer in the S frame is
  • a)
    1.6 C
  • b)
    1 .0 C
  • c)
    0.975 C
  • d)
    0.875 C
Correct answer is option 'C'. Can you explain this answer?
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An electron is moving in the positive X direction, in S frame. The rel...
The relative relativistic velocity is given as

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An electron is moving in the positive X direction, in S frame. The rel...
Given information:
- The electron is moving in the positive X direction in the S frame.
- The relative velocity between the S and S frames is 0.8c.
- The velocity of the electron is also 0.8c with respect to an observer in the S frame.

Explanation:
To solve this problem, we need to understand how velocities add up in special relativity. According to Einstein's theory of relativity, velocities do not simply add up like they do in classical physics. Instead, we use the relativistic velocity addition formula, which takes into account the effects of time dilation and length contraction.

Relativistic velocity addition formula:
v = (u + v) / (1 + uv/c^2)

Where:
v = velocity of the electron with respect to the S frame
u = velocity of the electron with respect to the S' frame (relative velocity between S and S' frames)
v = relative velocity between the S' frame and the observer in the S frame (velocity of the electron with respect to the observer in the S frame)

Applying the formula:
Let's substitute the given values into the formula:
v = (0.8c + 0.8c) / (1 + (0.8c * 0.8c) / c^2)
v = (1.6c) / (1 + 0.64)
v = (1.6c) / 1.64
v ≈ 0.975c

Therefore, the velocity of the electron for an observer in the S frame is approximately 0.975c.

Answer:
Option C: 0.975c
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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 0.8 c and the velocity of the electron is also 0. 8 c with respect to an observer in S frame. The velocity of the electron for an observer in the S frame isa)1.6 Cb)1 .0 Cc)0.975 Cd)0.875 CCorrect answer is option 'C'. Can you explain this answer?
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