Question

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?
2 m/s, northwest
10 m/s, northwest
14 m/s, northwest
48 m/s, northwest

Answer 1

6^2 + 8^2 = 36 + 64 = 100

sqrt(100) = 10 m/s northwest

Answer 2

The correct answer to the question is : 10 m/s , northwest.

EXPLANATION:

As per the question, the velocity of wind V = 8 m/s towards north.

      The velocity of the paper airplane is V' = 6 m/s towards west.

We are asked to calculate the actual velocity of the airplane.

By putting Pythagorean theorem, the actual velocity of the airplane is calculated as -

                  $V_{net}^2 =\ V^2+V'^2$

                ⇒  $V_{net}^2=\ 6^2+8^2$

                ⇒  $V_{net}^2\ =\ 100$

                ⇒  $V_{net}=\ \sqrt{100}\ m/s$

                ⇒  $V_{net}=\ 10\ m/s$  towards northeast.

Hence, the correct answer is 10 m/s , northwest.