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The problem asks us to find the linear speed \( v \) for the tip of a propeller that is 3 meters long, rotating at 400 revolutions per minute. The hint suggests using \( r = 1.5 \, \text{m} \) as the radius.

### Step-by-step Solution:
1. **Determine the Circumference:**
   The propeller rotates in a circle. The formula for the circumference of a circle is:
   \[
   C = 2\pi r
   \]
   where \( r = 1.5 \, \text{m} \).

   Substituting:
   \[
   C = 2\pi \times 1.5 = 3\pi \, \text{m}
   \]

2. **Calculate the Linear Speed:**
   Linear speed \( v \) can be determined using the formula:
   \[
   v = \text{circumference} \times \text{number of rotations per minute}
   \]
   Given the number of rotations per minute is 400:
   \[
   v = 3\pi \times 400 = 1200\pi \, \text{m/min}
   \]

Thus, the linear speed is:
\[
v = 1200\pi \, \text{m/min}
\]

Would you like any more details or have questions? 

### Related Questions:
1. How does changing the radius affect the linear speed?
2. If the number of rotations per minute is halved, what happens to the linear speed?
3. What would be the linear speed in meters per second?
4. Can you calculate the angular speed of the propeller?
5. How would the result change if the propeller length increased to 4 meters?

**Tip:** The linear speed at the tip of a rotating object is directly proportional to both its radius and the number of rotations per unit time.

Find the linear speed v for the tip of a propeller 3 m long, rotating 400 times per minute (Hint: r = 1.5 m).

Learn how to calculate the linear speed for the tip of a propeller that is 3 meters long and rotates 400 times per minute. This example covers concepts in circular motion and linear speed calculations, ideal for high school students.

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