Chapter 15, Problem 40A

Lizzie is scooting down the Interstate at 17 percent of the speed of light and measures the distance between mileposts to be less than 5,280 feet.

a. What distance does she measure?

b. What distance would she measure at 32 percent the speed of light?

To determine

The distance between the measured mileposts.

Answer to Problem 40A

The distance between the measured mileposts is 5203 ft.

Explanation of Solution

Given:

The distance between mileposts is $L_0=5,280\text{ ft}$ .

The speed is $v=0.17c$ .

Formula used:

The expression for relativistic length contraction is,

  $L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Here, $L_0$ is the measured length of the object at rest, $v$ is the speed of the object relative to an observer, and $c$ is the speed of the light.

Calculation:

The distance between mileposts she measured is,

  $\begin{array}{l}L=L_0\sqrt{1-\frac{v^2}{c^2}}\\ L=\left(\text{5,280 ft}\right)\sqrt{1-\frac{{\left(0.17c\right)}^2}{c^2}}\\ L=5,203\text{ ft}\end{array}$

Conclusion:

Thus, the distance between the measured mileposts is $5,203\text{ ft}$ .

To determine

The distance between measured mileposts.

Answer to Problem 40A

The distance between the measured mileposts is 5002 ft.

Explanation of Solution

Given:

The distance between mileposts is $L_0=5,280\text{ ft}$ .

The speed is $v=0.32c$ .

Formula used:

The expression for relativistic length contraction is,

  $L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Here, $L_0$ is the measured length of the object at rest, $v$ is the speed of the object relative to an observer, and $c$ is the speed of the light.

Calculation:

The distance between the measured mileposts is,

  $\begin{array}{l}L=L_0\sqrt{1-\frac{v^2}{c^2}}\\ L=\left(\text{5,280 ft}\right)\sqrt{1-\frac{{\left(0.32c\right)}^2}{c^2}}\\ L=5,002\text{ ft}\end{array}$

Conclusion:

Thus, the distance between the measured mileposts is $5,002\text{ ft}$ .