How does relativistic velocity addition work
GeneralClass 12AllAnswered 27 Mar 2026
Answer
Unlike classical physics, velocities don't simply add at high speeds. The relativistic formula is:
v = (v₁ + v₂)/(1 + v₁v₂/c²)
where c is the speed of light.
Why this matters:
- Classical: If you throw a ball at 10 m/s from a train moving 20 m/s, ball speed = 30 m/s ✓
- Relativistic: If spaceship A moves at 0.9c and fires a projectile at 0.9c, projectile speed ≠ 1.8c
- Using the formula: v = (0.9c + 0.9c)/(1 + 0.81) = 1.8c/1.81 ≈ 0.994c (still less than light speed!)
Note: At everyday speeds, v₁v₂/c² is negligible, so the formula reduces to classical addition. Relativistic effects only become significant above about 10% of light speed.
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