Two particles are moving in opposite directions each other with speed of 0.9c in laboratory frame of reference. the relative velocity of one particle to other is.?

Question

Answer

Understanding Relative Velocity
When two particles move toward each other at relativistic speeds, calculating their relative velocity involves the principles of special relativity.
Given Information
- Speed of Particle A = 0.9c (toward Particle B)
- Speed of Particle B = 0.9c (toward Particle A)
Relative Velocity Formula
To find the relative velocity (v_rel) of one particle with respect to the other, we use the relativistic velocity addition formula:
v_rel = (v1 + v2) / (1 + (v1 * v2 / c^2))
Where:
- v1 = speed of Particle A = 0.9c
- v2 = speed of Particle B = 0.9c
- c = speed of light
Substituting Values
- v_rel = (0.9c + 0.9c) / (1 + (0.9c * 0.9c / c^2))
Calculation Steps
- v_rel = (1.8c) / (1 + 0.81)
- v_rel = (1.8c) / (1.81)
Final Result
- v_rel ≈ 0.9945c
Conclusion
The relative velocity of one particle to the other, when both are moving at 0.9c in opposite directions, is approximately 0.9945c. This demonstrates how the effects of relativity significantly alter perceived velocities at high speeds.

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