The direction of the pigeon's resultant vector is 26° north of east. showing that the pigeon is not flying directly north but is being slightly deflected by the wind towards the east.
We start by resolving the pigeon's velocity vector into horizontal and vertical components:
Pigeon's horizontal velocity component: 40 mph * cos(0°) = 40 mph
Pigeon's vertical velocity component: 40 mph * sin(0°) = 0 mph
We then resolve the wind's velocity vector into horizontal and vertical components:
Wind's horizontal velocity component: 18 mph * cos(200°) = -15.6 mph
Wind's vertical velocity component: 18 mph * sin(200°) = 12.2 mph
The resultant horizontal velocity component: 40 mph - 15.6 mph
= 24.4 mph
The resultant vertical velocity component: 0 mph + 12.2 mph
= 12.2 mph
The magnitude = √(24.4 mph² + 12.2 mph²) = 26.5 mph
Direction= arctan(12.2 mph / 24.4 mph) = 26°
complete question:
A pigeon is flying north at 40 mph but the wind is blowing 20 south of west at 18 mph What is the direction of the pigeon's resultant vector?