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# Vector problem

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.

### 1 Answer

- 天同Lv 77 years agoFavorite Answer
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.