Chapter 26, Problem 5P

To determine

The speed from the time dilation.

Answer to Problem 5P

  $0.773c$

Explanation of Solution

Given info:

Rest time is $2.60\times {10}^{-8}m/s$ .

Time is $4.10\times {10}^{-8}s$ .

Formula used:

  $\Delta t=\frac{\Delta t_0}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

Where,

  $t_0$ is rest time

  $t$ is time

  $v$ is velocity

  $c$ is speed of light, $\left(3.00\times {10}^{8}m/s\right)$

Calculation:

Substitute the given values in the formula $\Delta t=\frac{\Delta t_0}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

  $4.10\times {10}^{-8}s=\frac{2.60\times {10}^{-8}s}{{\left[1-{\left(\frac{v}{3.00\times {10}^{8}m/s}\right)}^2\right]}^{\frac{1}{2}}}$

  $v=0.773c$

Conclusion: The required value is $0.773c$ .