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To convert 32 m/s into mph using the given conversion of \( 8 \, \text{km/h} = 5 \, \text{mph} \), let's follow these steps:

1. **Convert 32 m/s to km/h:**
   Since 1 m/s is equal to 3.6 km/h, we can multiply 32 m/s by 3.6 to get the speed in km/h.
   \[
   32 \, \text{m/s} \times 3.6 \, \frac{\text{km/h}}{\text{m/s}} = 115.2 \, \text{km/h}
   \]

2. **Use the conversion factor to convert km/h to mph:**
   The conversion provided is \( 8 \, \text{km/h} = 5 \, \text{mph} \). To convert 115.2 km/h to mph, we can use the ratio:
   \[
   \frac{5 \, \text{mph}}{8 \, \text{km/h}} = \frac{x \, \text{mph}}{115.2 \, \text{km/h}}
   \]
   Solving for \( x \):
   \[
   x = \frac{5 \times 115.2}{8} = 72 \, \text{mph}
   \]

So, \( 32 \, \text{m/s} \) is equivalent to **72 mph**.

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How would you convert 50 m/s to mph?
2. What is the conversion factor for km/h to m/s?
3. How would you convert mph to km/h if the conversion factor was \(1.6 \, \text{km/h} = 1 \, \text{mph}\)?
4. What is 10 m/s in mph using the same conversion rate?
5. If you had a speed of 120 mph, how would you convert it to m/s?

**Tip:** When converting speeds, always ensure the units are consistent before applying the conversion factor.

Use the conversion 8 km/h = 5 mph to convert 32 m/s into mph.

Learn how to convert 32 m/s to mph using the given conversion factor (8 km/h = 5 mph). This problem involves unit conversion and proportionality, key concepts in physics and mathematics, suitable for high school students in Grades 10-12.

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