How Do Wind and Plane Speeds Combine to Affect Ground Velocity?

[rossel]

Hi, I am having troubles with a question concerning relative motion. The problem goes:

A plane is traveling at an air speed of 285 km/h [E45ºS]. A wind is blowing to the northeast at 75 km/h [N22ºE] relative to the ground. Determine the velocity relative to the ground.

My teach prefers that we do not use the cosine law to determine the unknown vector, and instead requests that when we draw our diagram, we do something called the resolution of vectors. Which is separating the two vectors into x and y components, add the x's and y's together and use Pythagorean theorum to solve.

The cosine law provided me with the correct answer for this question, which was 265 km/h.

However, in using his method, my diagram (which was correct, and I have attached, to anyone who is confused), resembled a rectangle, and I came up with these calculations:

285/sin90 = x1/sin45
x1 = 202 km/h

x2/sin22 = 75/sin90
x2 = 28 km/h

Therefore, shouldn't x1 + x2 = 265 km/h ?
Please help me!

 

[learningphysics]

Yeah, I'm confused by your diagram. Your directions don't look right (which way on the diagram is north?). Plus you haven't drawn the vectors as being added.

To add vectors... suppose your adding a vector B to vector A... The tail (part without the arrow) of B has to be placed at the head (part with the arrow) of A.

Draw the diagram again.