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標題:

Vector problem

發問:

Airplane A flies due east at 245 km/h relative to the ground. At the same time, airplane B flies 315 km/h, 32 deg north of east relative to the ground. Determine the magnitude and direction of the velocity of Airplane A relative to B.

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最佳解答:

Resolve velocity of plane B in the northern and eastern direction components Northern component = 315.sin(32) km/h = 166.9 km/h Eastern component = 315.cos(32) km/h = 267.1 km/h The relative velocity of plane A relative to plane B... in the northern direction = 0 - 166.9 km/h = -1669. km/h (the -ve sign indicates that the direction is due south) in the eastern direction = (245 - 267.1) km/h = -22.1 km/h (the -ve sign indicates that the direction is due west) Hence, magnitude of relative velocity = square-root[166.9^2 + 22.1^2] km/h = 168.4 km/h Let a be the angle between the relative velocity and the western direction tan(a) = 166.9/22.1 a = arc-tan(166.9/22.1) = 82.5 degrees The velocity of plane A relative to plane B is 82.5 degrees south of west.

其他解答:31C9A75CB3B14398