a small plane heads west at 320 kph. there is a north wind blowing at 24 kph. what is the velocity (2 parts!) of the plane with respect to the ground?

would the answer be 320.9 kph? but there are two parts to the answer. what is the other part?

velocity has two components,

1. magnitude, your answer is correct for that
2. direction
look at your triangle, it was clearly right-angled, and you found the length of the hypotenuse
Now, can you find one of the acute angles ?
(hint: tangent)

would it be approximately 4.29°?

Yes, make sure your wording of the answer matches your diagram.

I don't know which method you use to state direction angles, but it could be called
W 5.29° S

To find the velocity of the plane with respect to the ground, we need to consider the effect of both the plane's velocity and the wind. Since the plane is heading west, its velocity is in the opposite direction of its destination.

First, let's calculate the component of the plane's velocity that is affected by the wind. Since the wind is blowing from the north, it does not directly affect the plane's east-west velocity. Instead, it affects the plane's north-south velocity. We can calculate this component using vector addition.

The plane's east-west velocity is 320 kph, and the wind's north-south velocity is 24 kph (remember the opposite direction).

Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
V^2 = (320^2) + (24^2)
V^2 = 102,400 + 576
V^2 = 102,976
V ≈ √102,976
V ≈ 320.9 kph

Therefore, the magnitude of the velocity of the plane with respect to the ground is approximately 320.9 kph.

Now, let's determine the direction of the plane's velocity with respect to the ground. Since the wind is blowing from the north, it is causing the plane to be pushed southward. Therefore, the second part of the answer is the direction, which can be stated as "south."

So, the complete velocity of the plane with respect to the ground is approximately 320.9 kph to the south.