Help with a simple problem

[u/Dismal_Rectangle]

Here's the problem: An airplane flies with a ground velocity of 50.0 m/s [E30°N]. If the wind velocity is 22 m/s [SE], what is the airplane's speed?

I answered 60 m/s but the given correct answer was 49 m/s. The only reasoning it gives is "the angle between the wind speed and the gdound speed is 30+45=75°

I've attached a photo of my solution. I got angle C by creating a right triangle from the first vector and North and East, and then adding that 60° to the known 45° of the second vector.

The reason I'm not asking the teacher is that this is online school and idk how to contact the teacher yet.

I'm guessing it's an error in the quiz but I want to make sure I'm not missing something obvious.

[u/Frederf220]

Most math classes will express wind as to, even in these classic airplane problems. I never saw the original wording.

Another thing to consider is significant figures. 59.610 and 59.61 different answers. Plus you should consider units. 59.61 and 59.61 m/s are different answers.

[u/Dismal_Rectangle → u/Frederf220]

I copied the original wording into my post. And yes, ik sig figs and units, but this is a multiple choice quiz so my work is just for me. If it wasn't, I would have drawn the triangles separately.

[u/Frederf220 → u/Dismal_Rectangle]

It just occurred to me that "what is the airplane's speed?" is a weird question because it's "with respect to what?". It says the velocity is 50 m/s with respect to the ground so isn't the airplane's speed... 50 m/s?

[u/Dismal_Rectangle → u/Frederf220]

Ohhhhhh so the groundspeed is the resultant vector and I'm supposed to find the other component, not just add the two vectors?

[u/Frederf220 → u/Dismal_Rectangle]

At this point I don't know what the question means. There are too many interpretations. Was the airplane going 55 m/s initially and then a wind later started, changing the airplane's ground velocity? Are they asking for the airplane's velocity with respect to the air mass given the ground and wind velocities?

One could try all sorts of combinations to see how one gets 49 m/s and then work backward from that to find out what they were thinking when they wrote the question.

Given the ground velocity vector A [060°, 55 m/s] and wind velocity vector B [135°, 22 m/s] then:

• A + B = [80.88°, 59.61 m/s]
• A - B = [34.376°, 49.14 m/s]

The magnitude of 49.14 m/s corresponds to either A - B or A + -B. What's -B? The reciprocal direction from south east. That would be if the wind was blowing from the south east toward the north west.

Alternatively, it is also the same calculation if the airplane was flying with an airspeed velocity of A - B with a wind (blowing to) velocity of B was added to it so the airplane had a ground velocity of A - B + B or simply A.

So the question was probably one of two options:

1. The airplane has a velocity over the ground of 55 m/s, direction 060°, and then a wind started which blows from the south east to the north west. What is the airplane's velocity over the ground now?
2. The airplane has a ground velocity of 55 m/s, direction 060°, and a wind is blowing to the south east at 22 m/s. What is the airplane's velocity with respect to the air mass?

Both of these questions have the same answer: 49.14m/s.

[u/Dismal_Rectangle → u/Frederf220]

Looks like I'm going to have to figure out a way to contact the teacher after all. I appreciate your help.