**Problem 27:** A radar signal took 2.7 seconds to travel to the moon and back. How far away was the moon at that time?To determine the distance between the Earth and the moon, we can use the speed of light, which is approximately $299,792,458$ meters per second. The total travel time for the radar signal is 2.7 seconds.The formula to calculate the distance $d$ is:\[ d = \frac{{\text{speed of light} \times \text{time}}}{2} \]Substituting the known values:\[ d = \frac{{299,792,458 \, \text{m/s} \times 2.7 \, \text{s}}}{2} \]By performing the calculation, you arrive at the approximate distance from Earth to the moon at that time. The image demonstrates the electromagnetic spectrum, showcasing the relationship between frequency (f) and wavelength (λ). **Top Axis (Frequency):** - The axis shows the frequency in hertz (Hz), increasing from left to right.- The frequency scale ranges from $10^2$ Hz (low frequency) to $10^{24}$ Hz (high frequency).**Bottom Axis (Wavelength):**- The axis depicts wavelength in meters (m), decreasing from left to right.- The wavelength scale ranges from $10^6$ m (long wavelength) to $10^{-14}$ m (short wavelength).**Regions of the Electromagnetic Spectrum:**- **Radio Waves:** Located at the leftmost part, characterized by low frequency and long wavelength. Includes AM, FM, and TV waves.- **Microwave:** Higher frequency and shorter wavelength than radio waves. Includes radar waves.- **Infrared:** Positioned after microwaves with shorter wavelengths.- **Visible Light:** Small segment in the middle, ranging from 700 nm (red) to 400 nm (violet).- **Ultraviolet:** Follows visible light, having yet higher frequencies and shorter wavelengths.- **X-rays:** Come after ultraviolet, with even more elevated frequencies.- **Gamma ($\gamma$) Waves:** At the rightmost end, featuring the highest frequency and shortest wavelength, described as high f, short λ.**Visible Light Spectrum:**- An enlarged section shows the visible light spectrum in detail, indicating colors corresponding to wavelengths from 700 nm (red) to 400 nm (violet). This diagram effectively illustrates how electromagnetic waves vary across different regions in terms of frequency and wavelength.

We are given a radar signal. A radar signal is nothing but an electromagnetic wave. We know that all electromagnetic wave travel at speed of light. We are given time of return trip of signal from moon. We find distance of moon from us.Speed of signal is c=3×108m/s Time taken for return trip is t=2.7s Let the distance of moon be d. Hence we have t=2dcd=ct2d=3×2.7×1082d=4.05×108 m This is distance of moon at that time.

Answered: 27. A radar signal took 2.7 seconds to…

Science

Physics

27. A radar signal took 2.7 seconds to go to the moon and return. How far away was the moon at that time?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Special Relativity

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances.

Question

**Problem 27:** A radar signal took 2.7 seconds to travel to the moon and back. How far away was the moon at that time?

To determine the distance between the Earth and the moon, we can use the speed of light, which is approximately $299,792,458$ meters per second. The total travel time for the radar signal is 2.7 seconds.

The formula to calculate the distance $d$ is:
\[ d = \frac{{\text{speed of light} \times \text{time}}}{2} \]

Substituting the known values:
\[ d = \frac{{299,792,458 \, \text{m/s} \times 2.7 \, \text{s}}}{2} \]

By performing the calculation, you arrive at the approximate distance from Earth to the moon at that time.

The image demonstrates the electromagnetic spectrum, showcasing the relationship between frequency (f) and wavelength (λ).

**Top Axis (Frequency):**
- The axis shows the frequency in hertz (Hz), increasing from left to right.
- The frequency scale ranges from $10^2$ Hz (low frequency) to $10^{24}$ Hz (high frequency).

**Bottom Axis (Wavelength):**
- The axis depicts wavelength in meters (m), decreasing from left to right.
- The wavelength scale ranges from $10^6$ m (long wavelength) to $10^{-14}$ m (short wavelength).

**Regions of the Electromagnetic Spectrum:**
- **Radio Waves:** Located at the leftmost part, characterized by low frequency and long wavelength. Includes AM, FM, and TV waves.
- **Microwave:** Higher frequency and shorter wavelength than radio waves. Includes radar waves.
- **Infrared:** Positioned after microwaves with shorter wavelengths.
- **Visible Light:** Small segment in the middle, ranging from 700 nm (red) to 400 nm (violet).
- **Ultraviolet:** Follows visible light, having yet higher frequencies and shorter wavelengths.
- **X-rays:** Come after ultraviolet, with even more elevated frequencies.
- **Gamma ($\gamma$) Waves:** At the rightmost end, featuring the highest frequency and shortest wavelength, described as high f, short λ.

**Visible Light Spectrum:**
- An enlarged section shows the visible light spectrum in detail, indicating colors corresponding to wavelengths from 700 nm (red) to 400 nm (violet).

This diagram effectively illustrates how electromagnetic waves vary across different regions in terms of frequency and wavelength.

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