Chapter 5, Problem 54A

Interpretation Introduction

Interpretation:

Time taken by a radio signal from the Voyager spacecraft to reach Earth needs to be determined, if the distance between Voyager and Earth is $2.72\times {10}^{9}km.$

Concept introduction Radio signals travel with the light’s speed so the time taken to travel can be calculated by distance traveled divided by the speed.

Answer to Problem 54A

151 min.

Explanation of Solution

Given: Distance between Voyager and Earth is $2.72\times {10}^{9}km.$

Explanations:

Velocity = distance/time

The given distance is as follows:

$d=2.72\times {10}^9\text{ km}\left(\frac{1000\text{ m}}{1\text{ km}}\right)$

Or,

$=2.72\times {10}^{12}m$

Radio signals travel with the light’s speed so the time taken to travel can be calculated by distance traveled divided by the speed.

$\text{Time=}\frac{\text{distance}}{\text{speed}}$

Putting the values,

$\begin{array}{l}\text{Time}=\frac{2.72\times {10}^{12}\text{ m}}{3.00\times {10}^8\text{ m/s}}\\ =9070s\left(\frac{1\text{ min}}{60\text{ s}}\right)=151\text{ min}\end{array}$

Conclusion

Time taken by a radio signal from the Voyager spacecraft to reach Earth is 151 min.