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.
- 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.