https://file.aiquickdraw.com/mathbot/file/1726016552214ev1vx2hc.jpg

Let me first transcribe the text from the image and proceed to solve the problems.

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**Transcription:**

1. En 2012, Voyager 2 est devenue la plus longue et la plus mythique mission de la NASA. Ses instruments continuent d'envoyer des observations après 41 années de voyage dans le système solaire. Chaque message de Voyager 2 met 16 heures et demi à atteindre la Terre. Combien de kilomètres séparaient la Terre de Voyager 2 à ce moment?

2. Voyager 2 est officiellement sortie du système solaire en novembre 2018, elle a atteint les limites de l’héliosphère située à environ 120 unités astronomiques de la Terre. En novembre 2019, Voyager était située à 135 unités astronomiques de la Terre. À quelle vitesse en m/s se déplace Voyager 2?

1 UA = 150 000 000 km

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Let's address each problem one by one.

### Problem 1:
- Time taken for Voyager 2's message to reach Earth: 16.5 hours
- Speed of light: 299,792 km/s

We will calculate the distance using the formula:  
\[
\text{Distance} = \text{Speed of light} \times \text{Time}
\]

Let's compute the answer.The distance between Earth and Voyager 2 in 2012, based on the time it takes for the signal to reach Earth, was approximately **17,807,644,800 kilometers**.

### Now, let's move to problem 2:

We are asked to find the speed of Voyager 2 in meters per second between November 2018 and November 2019. 

- In November 2018, Voyager 2 was 120 AU from Earth.
- In November 2019, Voyager 2 was 135 AU from Earth.
- 1 AU = 150,000,000 km.

We need to calculate the distance covered in 1 year (from 120 AU to 135 AU), and then convert it to meters per second. We'll follow these steps:

1. Calculate the difference in AU (distance covered in AU).
2. Convert this distance to kilometers.
3. Convert the time (1 year) to seconds.
4. Calculate the speed using the formula:
   \[
   \text{Speed} = \frac{\text{Distance}}{\text{Time}}
   \]

Let's compute this.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the speed of Voyager 2 in meters per second by following these steps:

1. **Distance traveled by Voyager 2**:  
   \( 135 \, \text{AU} - 120 \, \text{AU} = 15 \, \text{AU} \).  
   Since 1 AU = 150,000,000 km,  
   \( 15 \, \text{AU} = 15 \times 150,000,000 = 2,250,000,000 \, \text{km} \).

2. **Convert time to seconds**:  
   1 year ≈ 31,557,600 seconds (365.25 days per year).

3. **Speed in meters per second**:  
   Convert km to meters by multiplying by 1,000.  
   \[
   \text{Speed} = \frac{2,250,000,000 \times 1,000}{31,557,600} \approx 71,303 \, \text{m/s}
   \]

Let me know if you'd like any further clarification.

### Related Questions:
1. How far is Voyager 1 from Earth in comparison to Voyager 2?
2. What are the main objectives of the Voyager missions?
3. How do signals from Voyager 2 still reach Earth after traveling such distances?
4. Can Voyager 2 ever return to the solar system?
5. What type of data is Voyager 2 still sending back to Earth?

**Tip**: Astronomical units (AU) are commonly used in space measurements to simplify large distances like those between planets and stars.

1- En 2012, Voyager 2 est devenue la plus longue et la plus mythique mission de la NASA. Ses instruments continuent d'envoyer des observations après 41 années de voyage dans le système solaire. Chaque message de Voyager 2 met 16 heures et demi à atteindre la Terre. Combien de kilomètres séparaient la Terre de Voyager 2 à ce moment?

2- Voyager 2 est officiellement sortie du système solaire en novembre 2018, elle a atteint les limites de l’héliosphère située à environ 120 unités astronomiques de la Terre. En novembre 2019, Voyager était située à 135 unités astronomiques de la Terre. À quelle vitesse en m/s se déplace Voyager 2?

1 UA = 150 000 000 Km

This problem involves calculating the distance of Voyager 2 from Earth in 2012, using light travel time, and its speed in meters per second between 2018 and 2019 based on its position in astronomical units. Key concepts include speed of light, unit conversions, and distance calculations.

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