An airplane flies 200 km due west from city A to city B and then 305 km in the d

Question

An airplane flies 200 km due west from city A to city B and then 305 km in the direction of 29.5o north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? 365 Your response differs from the correct answer by more than 10%. Double check your calculations. km (b) Relative to city A, in what direction is city C? o north of west (c) Why is the answer only approximately correct? An airplane flies 200 km due west from city A to city B and then 305 km in the direction of 29.5o north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? 365 Your response differs from the correct answer by more than 10%. Double check your calculations. km (b) Relative to city A, in what direction is city C? o north of west (c) Why is the answer only approximately correct?

Explanation / Answer

a) x = 200 + (305 * cos 29.5) = 465.46 km

y = 0 + (305 * sin 29.5) = 150.19 km

d = sqrt [x2 + y2]  = sqrt [465.462 + 150.192]

= 489.1 km

b) tan theta = 150.19 / 465.46

theta = 17.88 deg [north of west]

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