Question

A private plane is traveling due east at a rate of 150 mph. A south wind is blowing 50 mph. What is the actual velocity of the plane?

(1 point)
Responses

approximately equal to 141mph
Image with alt text: approximately equal to 141 mph

approximately equal to 158mph
Image with alt text: approximately equal to 158 mph

approximately equal to 172mph
Image with alt text: approximately equal to 172 mph

approximately equal to 200mph
Image with alt text: approximately equal to 200 mph

Answer 1

To find the actual velocity of the plane, we can treat the situation as a vector problem. The plane's velocity and the wind's velocity are perpendicular to each other. We can use the Pythagorean theorem to compute the magnitude of the resultant velocity.

1. The velocity of the plane is 150 mph due east (let's call this vector \( V_p \)).
2. The wind's velocity is 50 mph due south (let's call this vector \( V_w \)).

The actual velocity \( V \) (resultant velocity) can be calculated using the Pythagorean theorem:

\[
V = \sqrt{V_p^2 + V_w^2}
\]

Substituting the values:

\[
V = \sqrt{(150)^2 + (50)^2}
\]
\[
V = \sqrt{22500 + 2500}
\]
\[
V = \sqrt{25000}
\]
\[
V \approx 158.11 \text{ mph}
\]

Thus, the actual velocity of the plane is approximately equal to 158 mph.

So the correct response is:

**approximately equal to 158mph**.