Question

Two electrons are moving in an opposite direction with speeds of $0.8c$ and $0.4c$, where $c$ is the speed of light in a vacuum. Then, the relative speed is about

• A. $0·4c$
• B. $0·8c$
• C. $0·9c$
• D. $1.2c$

Answer 1

The correct option is C

$0·9c$

The explanation for the correct option:

C: $0·9c$

Step 1: Given data

• Speed of the first electron$\left(v\right)=0.8c$
• Speed of the second electron$\left(u\right)=0.4c$

Step 2: Formula used

• The relative speed can be computed using the following formula:
• $v_{rel}=\frac{v+u}{1+{\displaystyle \frac{vu}{c^2}}}$

Step 3: Compute the relative speed

• Substitute the known values in the formula
• $\begin{array}{rcl}{v}_{rel}& =& \frac{v+u}{1+{\displaystyle \frac{vu}{c^2}}}\\ & =& \frac{0·8c+0·4c}{1+{\displaystyle \frac{0·8c\times 0·4c}{c^2}}}\\ & =& \frac{1·2c}{1+0.32}\\ & =& 0·9c\end{array}$

Final Answer: Hence, option (C) is the correct answer.