A commuter airplane starts from an airport and takes the route shown in the figu

Question

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° 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. distance _______km angle _______° west of north A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° 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. distance _______km angle _______° west of north distance _______km angle _______° west of north

Explanation / Answer

The first vector is 175*[cos(30) , sin(30)] = [151.5544 , 87.5 ] the second vector is 150*[cos(110) , sin(110)] = [ -51.3030 140.9539 ] the third is 190*[cosd(180), sind(180)] = [-190 , 0] Sum the three [x,y] components, you get: -89.7486 228.4539 magnitude = sqrt( 89.7486^2 + 228.4539^2 ) = 245.4506 angle west of north = atan(89.7486 / 228.4539) = 21.4475 degrees

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