Electronic communication via radio travels at approximately the speed of light (186,000 miles/second). The edge of the solar system is roughly at Pluto, which is 3.6 × 109 miles from Earth at its closest approach. How many hours does it take for a radio signal from Earth to reach Pluto?
A. 2.5 hrs B. 3.2 hrs C. 5.4 hrs D. 10 hrs
The Correct Answer and Explanation is :
To solve this problem, we need to calculate the time it takes for a radio signal, traveling at the speed of light, to reach Pluto.
Step 1: Determine the relevant values
- The speed of light is approximately 186,000 miles per second.
- The distance from Earth to Pluto at its closest approach is 3.6 × 10⁹ miles.
Step 2: Calculate the time it takes for the signal to reach Pluto
We can use the formula for time:
[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
]
Substitute the known values into the formula:
[
\text{Time} = \frac{3.6 \times 10^9 \text{ miles}}{186,000 \text{ miles/second}}
]
Step 3: Perform the division
[
\text{Time} = \frac{3.6 \times 10^9}{186,000} \approx 19,354.8 \text{ seconds}
]
Step 4: Convert the time from seconds to hours
There are 3,600 seconds in an hour, so:
[
\text{Time in hours} = \frac{19,354.8 \text{ seconds}}{3,600 \text{ seconds/hour}} \approx 5.39 \text{ hours}
]
Conclusion
The time it takes for a radio signal to travel from Earth to Pluto is approximately 5.4 hours. Therefore, the correct answer is:
C. 5.4 hrs
Explanation:
The calculation involves dividing the distance from Earth to Pluto by the speed of light, then converting the result from seconds to hours. The speed of light is so fast that even over the vast distance to Pluto, it still takes several hours for the signal to travel, showing the immense size of the solar system.