Question

A bird is flying south at a rate of

45 miles per hour while being
pushed east by wind with a
speed of 12 miles per hour.
What is the direction of the bird's
resultant vector?
Hint: Draw a vector diagram.
0 = [?] ³º ,
Round your answer to the nearest hundredth.

Answer 1

284.93°

Explanation:

If the bird is flying south, then it's flying in a direction of 270°

If the wind is moving east, then its direction angle is 0°

Therefore, we can write the bird and wind as vectors:

Bird -->
`u=45\langle\cos270^\circ,\sin 270^\circ\rangle=45\langle0,-1\rangle=\langle0,-45\rangle`

Wind -->
`v=12\langle\cos0^\circ,\sin 0^\circ\rangle=12\langle1,0\rangle=\langle12,0\rangle`

Now, add the horizontal and vertical components of the vectors respectively to get the resultant vector of the bird:

`u+v=\langle0,-45\rangle+\langle12,0\rangle=\langle0+12,-45+0\rangle=\langle12,-45\rangle`

The direction of the bird's resultant vector can be calculated in the following way:

`\theta=\tan^(-1)((y)/(x))=\tan^(-1)((-45)/(12))\approx-75.07^\circ=360^\circ-75.07^\circ=284.93^\circ`