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 30.00 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 245.s km 68.55 Your response differs from the correct answer by more than 100%. west of north angle 200 110 5100 150 200 Need Help? Read Talk to Tuter

Explanation / Answer

r1 = 175 (cos30i + sin30j)

r2 = 150 (-sin20i + cos20 j)

r3 = - 190 i

r = r1 + r2 + r3

r = (175 cos30 - 150 sin20 - 190)i + (175 sin30 + 150 cos20)j

displacement , r = - 89.75 i + 228.45 j

distance = |r| = sqrt(89.75^2 + 228.45^2)

= 245.5 km .....Ans

position is in 89.75 km in west and 228.45 km in north

so angle with north = tan^-1(west distance / north distance )

= tan^-1(89.75 / 228.45)

= 21.4 deg west of north ...Ans

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