3. An airplane flies 200 km due west from city A to city B and then 295 km in th

Question

3. An airplane flies 200 km due west from city A to city B and then 295 km in the direction of 24.5° north of west from city B to city C.

A force 1 of magnitude 5.00 units acts on an object at the origin in a direction θ = 43.0 degree above the positive x-axis. (See the figure below.) A second force 2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force 1 + 2. An airplane flies 200 km due west from city A to city B and then 295 km in the direction of 24.5 degree north of west from city B to city C. In straight-line distance, how far is city C from city A? Relative to city A, in what direction is city C? Why is the answer only approximately correct?

Explanation / Answer

F1 = 5cos(43) i + 5sin(43) j

F2 = 5j

resultant = 3.66 i - 8.41 j

magnitude = 9.2

angle with x axis = cos -(3.66/9.2) = 66.6 degrees

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