A plane can travel at 80 mi/hr with respect to the air. Determine the resultant velocity of
the plane (magnitude only) if it encounters a 15 mph crosswind.

To determine the resultant velocity of the plane when it encounters a crosswind, we can apply the Pythagorean theorem. The reason for this is that the velocity of the plane and the crosswind form a right triangle, where the plane's velocity and the wind speed are perpendicular.

### Given:
- Speed of the plane with respect to the air: \( 80 \, \text{mph} \)
- Speed of the crosswind: \( 15 \, \text{mph} \)

The resultant velocity \( V_r \) is the hypotenuse of this right triangle. Using the Pythagorean theorem:

\[
V_r = \sqrt{(80)^2 + (15)^2}
\]

Let’s calculate that.

\[
V_r = \sqrt{6400 + 225} = \sqrt{6625} \approx 81.41 \, \text{mph}
\]

### Result:
The resultant velocity of the plane is approximately **81.41 mph**.

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Would you like further clarification on any part of the calculation?

Here are 5 follow-up questions related to this topic:
1. What if the crosswind speed increases? How would it affect the resultant velocity?
2. How would a headwind or tailwind affect the plane's resultant velocity?
3. Can you calculate the direction (angle) of the resultant velocity?
4. How does air resistance factor into real-world flight conditions?
5. What are some examples of how pilots adjust for crosswinds during takeoff and landing?

**Tip:** In real-world scenarios, pilots often use trigonometric calculations to adjust the heading of the plane to compensate for crosswinds and maintain the desired course.

A plane can travel at 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a 15 mph crosswind.

Discover how to calculate the resultant velocity of a plane traveling at 80 mph with a 15 mph crosswind. This problem demonstrates the application of vector addition and the Pythagorean theorem, ideal for students in Grades 9-11.

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