Physics: Adding Vectors?

I have a question on a problem. I have attempted it and I havent gotten the answer. It is driving me insane. It is a vector problem and I found out the x and y components of each and the magnitude of each angle and I have not gotten the right answer for anything. The right answer is suppose to be 245km and I can not seem to get it. The question is:





A commuter airplane flies from the airport to city A, locate 175km away in a direction 30 degrees north of east. Next it flies for 150 km 20 degrees west of north to city B. Finally, the plane flies 190 km due west to city C. Find the location of city C relative to the location of the starting point.





Can someone please help me out? I know that the degree for the flight from city A to B is actually 110, so I'm doing that right and the degree for flight from city B to C is 0 because it just flies west. I tried adding component A +B+C and I can not find the magnitude from C to A...help!! Thanks in advance!

Physics: Adding Vectors?
i don't follow what you did.


here's how i did it:


let X be the point 175 km away at a 30 degree angle.


vector A-x: mag 175 x component 175 cos 30 = 152


and the y component is 175 sin 30 = 88





vector x-B: mag 150 x component -150sin20=-51


and the y component is 150cos20 = 141


vector B-C the y component is zero and


the x component is -190





so the location of C is:





x component : 152-51-190=-89


y component: 88 + 141 =229


so the resultant from A - C is sqrt[(89^2)(229^2)]= 246 km





and the angle is 110 degrees
Reply:The coordinates of city C are (175cos30+150cos110+190cos180, 175sin30+150sin110+190sin180), or (-89.75, 228.45).


Finish with the Pythagorean Theorem.

quince