(a) In communicating with an astronaut on the moon, 3.8 x 108 m from earth, what is the minimum time delay in getting a response to a question? (b) What would the minimum time delay be for communication with an astronaut at a distance of 2 light-years from earth?

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### Communication Time Delay with Astronauts

#### Problem Statement

**(a)** In communicating with an astronaut on the moon, \(3.8 \times 10^8\) meters from Earth, what is the minimum time delay in getting a response to a question?
- [Answer Box]

**(b)** What would the minimum time delay be for communication with an astronaut at a distance of \(2\) light-years from Earth?
- [Answer Box]

#### Explanation

To calculate the time delay in communication:

1. **For part (a):**
   - Distance to the moon: \(3.8 \times 10^8\) meters.
   - Speed of light (\(c\)): \(3 \times 10^8\) meters/second.
   - Time delay for a single trip (Earth to Moon): \( t = \frac{d}{c} = \frac{3.8 \times 10^8 \text{ meters}}{3 \times 10^8 \text{ meters/second}} \).
   - Minimum time delay for a response (Earth to Moon and back): \(2 \times t\).

2. **For part (b):**
   - Distance to the astronaut: \(2\) light-years.
   - Speed of light (\(c\)): One light-year is the distance light travels in one year.
   - Time delay for a single trip (Earth to astronaut): \(2\) years.
   - Minimum time delay for a response (Earth to astronaut and back): \(2 \times 2 = 4\) years.

These computations ensure that the correct time delays are assessed for communication with astronauts at various distances.
Transcribed Image Text:### Communication Time Delay with Astronauts #### Problem Statement **(a)** In communicating with an astronaut on the moon, \(3.8 \times 10^8\) meters from Earth, what is the minimum time delay in getting a response to a question? - [Answer Box] **(b)** What would the minimum time delay be for communication with an astronaut at a distance of \(2\) light-years from Earth? - [Answer Box] #### Explanation To calculate the time delay in communication: 1. **For part (a):** - Distance to the moon: \(3.8 \times 10^8\) meters. - Speed of light (\(c\)): \(3 \times 10^8\) meters/second. - Time delay for a single trip (Earth to Moon): \( t = \frac{d}{c} = \frac{3.8 \times 10^8 \text{ meters}}{3 \times 10^8 \text{ meters/second}} \). - Minimum time delay for a response (Earth to Moon and back): \(2 \times t\). 2. **For part (b):** - Distance to the astronaut: \(2\) light-years. - Speed of light (\(c\)): One light-year is the distance light travels in one year. - Time delay for a single trip (Earth to astronaut): \(2\) years. - Minimum time delay for a response (Earth to astronaut and back): \(2 \times 2 = 4\) years. These computations ensure that the correct time delays are assessed for communication with astronauts at various distances.
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