Calculating Resultant Velocity with Vector Addition

[tannye92]

Homework Statement

A novice pilot sets a plane's controls, thinking the plane will fly at 125km/hr to the north. If the wind blows 75km/hr toward the southeast, what is the plane's resultant velocity?
________ km/hr at ________° north of east.

Homework Equations

I don't know how to set this problem up apparently. I read the chapter in my book, but it doesn't give any examples that show how they got that answer for me to look at and figure out. I know I'm supposed to set up a triangle, but I don't know how I would go about finding the degrees or anything like that. Could someone work this sample problem out for me? I would like to know what I'm doing for when I take my test.

The Attempt at a Solution

(125)+(75) = 200 THIS ANSWER IS WRONG THOUGH.

 

[S_Happens]

You already know that you are given two vectors (magnitude and direction). So you have to set up a coordinate system to make them of any use. Since you are given the vector directions in terms of a compass, you already a familiar coordinate system.

Start from there and see if you can get anywhere.

 

[tannye92]

Okay, I kind of get what you're saying, but I'm still lost. I read about it being like a compass in my physics book, but I don't know what I'm supposed to do to start it. We just finished covering the section with acceleration and velocity. Formulas I can do. This stuff I'm a complete idiot at. I just don't get it and my teacher can't be reached fast enough (online class). :(

 

[dayyou]

Try thinking in terms of the real world. If you are walking at 15 mph, and a 3 mph gust of wind hits you from the front, do you feel more resistance or less (ie, would you add the 3 mph or subtract it)?

 

[tannye92]

I tried subtracting 75 from 125 and getting 50, but that's wrong too. Still lost with how to solve this problem.

 

[S_Happens]

(ie, would you add the 3 mph or subtract it)?

I this last part is unneccessary and possibly confusing. In this problem it's all vector addition and simply applying the correct coordinate system (and therefore direction). A better example would be with a tailwind, or some description that doesn't include subtraction. In the end you reach the same answer, but if you can handle this without pure vector addition, then you've already mastered the concepts beyond needing help.

To the OP, your coordinate system will look like a compass. You will start in the middle. The plane is moving in a certain direction at a certain speed and the wind is blowing in a different direction at a certain speed. You can take both vectors into account seperately and come up with a third vector that gives you the REAL speed/direction of the plane.

I'll change dayyou's example to be walking at 15 mph (more like sprinting), but with a 3 mph wind at your back. Both vectors are in the same direction, so it's as simple as adding them together (18 mph in the direction the person is walking). If it was a wind that was blowing directly from the side of the walking person, they would still have a forward speed of 15 mph, but would also be pushed to the side. Combining the two vectors would result in the actual speed/direction of the walker. The triangle that you need to form is those two vectors added together to make a third. In the example with the wind at the back, the third side of the triangle is simple laid over the other two legs (so there's no real triangle).

I don't think I can give anymore without totally answering it for you, so at least try to piece it together. Don't just play with the numbers, but draw a compass and try putting the vectors for the airplane and wind on it.

 

[dayyou]

S_Happens definitely put what I was trying to convey into words that actually made sense, haha.

 

[tannye92]

I am trying to piece this together, but I just don't understand. I don't want you to work the problem for me. I'm not asking for that. There's got to be a formula for this problem that I don't see. Still not getting it.

 

[S_Happens]

It is vector addition. A simple A + B = C, where A and B are your original vectors and C is the resultant vector. Because vectors have a magnitude and direction you must specificy a useful coordinate system, in this case the layout of a compass (N,W,S,E).

This is where you get your triangle and will have to figure out the new direction and magnitude which is the answer you're looking for.