An electron moves to the right with a speed of 0.93 c relative to the laboratory frame. A proton...

Question:

An electron moves to the right with a speed of {eq}0.93\ c {/eq} relative to the laboratory frame. A proton moves to the left with a speed of {eq}0.63\ c {/eq} relative to the electron. Find the speed of the proton relative to the laboratory frame.

Relative Velocity in Fast Moving Systems

According to the theory of relativity, the relative velocity of a fast moving particle with respect to another moving object is given by:

{eq}\displaystyle u'=\frac{u-v}{1-\frac{uv}{c^2}} {/eq}

Where,

  • {eq}u' {/eq} is the velocity of the particle with respect to the moving frame,
  • {eq}u {/eq} is the velocity of the particle with respect to rest frame,
  • {eq}v {/eq} is the velocity of the moving frame with respect to the rest frame and
  • {eq}c=3.00\times10^8\ m/s {/eq} is the speed of light.

Answer and Explanation:

Given:

{eq}u=0.93c\\ u'=0.63c {/eq}

The velocity of proton with respect to laboratory frame is,

{eq}\displaystyle v=\frac{u'-u}{\frac{u'u}{c^2}-1}=\frac{0.63c-0.93c}{\frac{0.63c\times0.93c}{c^2}-1}=0.72c {/eq}


Learn more about this topic:

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Theory of Relativity: Definition & Example

from Remedial Algebra I

Chapter 25 / Lesson 1
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