If you stood on Earth during its formation, during which it captured about 2.1 x 1011 particles per second, and watched a region covering 260 m2, how many impacts would you expect to see in an hour? (Notes: The surface area of a sphere is 4tr?. Hint: Assume that Earth had its current radius of 6,378 km.) impacts

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There is only one part to this question and I need to know the impacts. Thank you!!

**Problem Statement:**

If you stood on Earth during its formation, during which it captured about \(2.1 \times 10^{11}\) particles per second, and watched a region covering \(260 \, \text{m}^2\), how many impacts would you expect to see in an hour? 

*(Notes: The surface area of a sphere is \(4\pi r^2\). Hint: Assume that Earth had its current radius of 6,378 km.)*

**Input Box:**

[            ] impacts

**Detailed Explanation:**

To solve the problem, you need to calculate the number of particle impacts on a specified area over a given time. 

1. **Calculate the Total Surface Area of the Earth:**

   - The formula for the surface area of a sphere is \(4\pi r^2\).
   - Given the radius \(r = 6,378 \, \text{km}\), convert it to meters for consistency: \(r = 6,378,000 \, \text{m}\).
   - Substitute the value: \( \text{Surface Area} = 4\pi (6,378,000 \, \text{m})^2\).

2. **Determine Impacts Per Second:**

   - Total particles captured per second by the Earth = \(2.1 \times 10^{11}\).

3. **Calculate the Impacts for the Selected Area:**

   - Find the proportion of impacts for \(260 \, \text{m}^2\) by using the ratio of the selected area to the total surface area.
   - \( \frac{260 \, \text{m}^2}{\text{Surface Area of Earth}} \times (2.1 \times 10^{11}) = \text{Impacts per second on 260} \, \text{m}^2\).

4. **Calculate the Expected Impacts in an Hour:**

   - Multiply the impacts per second by the number of seconds in an hour (3600 seconds) to find the total impacts in one hour.

Putting these steps together, you can determine the expected number of impacts.
Transcribed Image Text:**Problem Statement:** If you stood on Earth during its formation, during which it captured about \(2.1 \times 10^{11}\) particles per second, and watched a region covering \(260 \, \text{m}^2\), how many impacts would you expect to see in an hour? *(Notes: The surface area of a sphere is \(4\pi r^2\). Hint: Assume that Earth had its current radius of 6,378 km.)* **Input Box:** [ ] impacts **Detailed Explanation:** To solve the problem, you need to calculate the number of particle impacts on a specified area over a given time. 1. **Calculate the Total Surface Area of the Earth:** - The formula for the surface area of a sphere is \(4\pi r^2\). - Given the radius \(r = 6,378 \, \text{km}\), convert it to meters for consistency: \(r = 6,378,000 \, \text{m}\). - Substitute the value: \( \text{Surface Area} = 4\pi (6,378,000 \, \text{m})^2\). 2. **Determine Impacts Per Second:** - Total particles captured per second by the Earth = \(2.1 \times 10^{11}\). 3. **Calculate the Impacts for the Selected Area:** - Find the proportion of impacts for \(260 \, \text{m}^2\) by using the ratio of the selected area to the total surface area. - \( \frac{260 \, \text{m}^2}{\text{Surface Area of Earth}} \times (2.1 \times 10^{11}) = \text{Impacts per second on 260} \, \text{m}^2\). 4. **Calculate the Expected Impacts in an Hour:** - Multiply the impacts per second by the number of seconds in an hour (3600 seconds) to find the total impacts in one hour. Putting these steps together, you can determine the expected number of impacts.
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