Question

(20 points)
Use the Pythagorean theorem to answer this question. A paper airplane is thrown westward at a rate of 6 m/s. The wind is blowing at 8 m/s toward the north. What is the actual velocity of the airplane?

Answer 1

The actual velocity of the airplane is 10 m/s at 53.1 degrees north of west

Explanation:

The actual velocity of the airplane can be found using Pythagorean's theorem: in fact, the velocity of the airplane and the velocity of the wind are perpendicular to each other, so they form the sides of a right triangle, of which the hypothenuse corresponds to the actual velocity.

We have:

- Velocity of the airplane: 6 m/s west

- Velocity of the wind: 8 m/s north

Therefore, applying Pytagorean's theorem, the magnitude of the actual velocity of the plane is:

$v=\sqrt{v_1^2+v_2^2}=\sqrt{8^2+6^2}=10 m/s$

The direction of the airplane instead  can be found by using:

$\theta=tan^{-1}(\frac{v_2}{v_1})=tan^{-1}(\frac{8}{6})=53.1^{\circ}$

And the direction is north of west.

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Answer 2

Answer:

10 m/s at 53.1 degrees

Explanation: