The direction of the pigeon's resultant vector is 6.18° north of east. showing that the pigeon is not flying directly north but is being slightly deflected by the wind towards the east.
What is the direction of the resultant?
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(20°) = 16.91 mph
Wind's vertical velocity component: 18 mph * sin(20°) = 6.16 mph
The resultant horizontal velocity component: 40 mph + 16.91 mph
=56.91 mph
The resultant vertical velocity component: 0 mph + 6.16 mph
= 6.16 mph
The magnitude is given as 37.84 mph
Direction= arctan(6.16 mph / 56.91 mph) = 6.18°