Question

Hi, I'm doing some review for my physics mid term and found this question for relative velocity that I cannot seem to understand.

For the case of a wind blowing from the east at 80 km/h and a plane capable of flying at 200 km/h, find...

the velocity of the plane relative to the ground if the pilot points the plane [N20°W] (give answer in m/s).

The answer is 52.30 m/s [E86°N].

If someone can guide me in the workings, that would be really great as I am struggling in understanding why this is the answer.

Thanks and Happy New Year!

Answer 1

I'm guessing that (N20degW) is like 90deg+20deg=110deg ??

Answer 2

well i mean it is going 20° West of North. But I think that is right. I made a picture if that can help?

Answer 3

yes, so it's 90+20=110 from the normal zero of the unit circle, right?

Answer 4

yes.

Answer 5

well since this is about relative speed to the ground, it sounds like we need to add the wind speed vectorially with the plane.
That means breaking into components. Did you do that?

Answer 6

if you mean by vector components I made it so Vpa (plane relative to air) = 200km/h [?]
Vag (air relative to ground) = 80km/h [W]
Vpg (plane relative to ground) = ? [N20°W]

Vpg = Vpa + Vag

Is this what you were talking about? I don't know if this is correct though.

Answer 7

the plane is at 110
so breaking the vector into components means we will find the "length" of the legs of the right triangle it forms:is this a completely new idea to you?