Chapter 26, Problem 20Q

To determine

Is our intuitive notion that velocities simply add as is section 3-8 completely wrong

Answer to Problem 20Q

Solution:

It can be need to speed of light with respect to earth $=c$

Explanation of Solution

Given:

Velocities simply add as is section 3-8 completely wrong

Speed of light the nearing speed at apply not do not simply velocities that notion indicative reference frames different Einstein showed that length correct formula for velocity

$u=\frac{v+u\text{'}}{1+\frac{vu\text{'}}{c^2}}$

For motion along a straight line

The above equation reduces to the classical form for velocities small compared to the speed of $light\sin ce\left(1+\frac{vu\text{'}}{c^2}\right)1andu\text{'}<c$

Thus $u=v+u\text{'}$

The above equation can be checked for the speed of light

Suppose $v=0.60c\text{'}qand$

$\begin{array}{l}u\text{'}=c\\ u=\frac{0.60c+c}{1+\frac{(0.60c)c}{c^2}}\\ =\frac{1.60c}{1.60}\\ u=c\end{array}$

Therefore, speed of light with respect to earth $=c$

This is fully consistent with the second postulate of relatively