PreCalculus Questions

Question

An airplane has an airspeed of 530 kilometers per hour bearing N30°E. The wind velocity is 20 kilometers per hour in the direction N40°W. By finding the resultant vector representing the path of the plane relative to the ground, what is the ground speed of the plane?

549.7 km/h
530.4 km/h
523.5 km/h
537.2 km/h

Answer 1

Convert vectors to rectangular form then add. For the plane, its vector makes a 60 degree angle with the positive x-axis, so point A (head of its vector) is 530(cos60, sin 60). The wind makes a 130 degree angle with the positive x-axis, so point B (head of its vector) is 20(cos 130, sin 130).

The resultant of P = A + B is:

(530cos60 + 20 cos 130, 530 sin60 + 20 sin 130) or (252.144248,474.314353). To find the magnitude of the vector from (0,0) to P is √(P.x²+P.y²) ≈ 537.16927224.

Visit this graph to see the vectors. Scroll out to see the endpoints of the two "long" vectors.

desmos.com/3d/zhiyfsbhvd