# Relative Velocity Bird Flying Problem

1. Aug 7, 2006

### danago

Hey. Ive done this question, but my answer is only partly correct according to the answer book. Heres the question:

"To a bird flying at 20km/h on a bearing of 160 degrees, the wind seems to be coming from the south at 25km/h. Find the true velocity of the wind"

ok. I said that B is the velocity of the bird, W is the velocity of the wind, and O is the origin. I then found that:

$$\begin{array}{l} \overrightarrow {OB} = \left( {\begin{array}{*{20}c} {20\cos 70} \\ { - 20\sin 70} \\ \end{array}} \right) \\ \overrightarrow {BW} = \left( {\begin{array}{*{20}c} 0 \\ {25} \\ \end{array}} \right) \\ \end{array}$$

I then said that:
$$\begin{array}{l} \overrightarrow {BW} = \overrightarrow {BO} + \overrightarrow {OW} \\ \left( {\begin{array}{*{20}c} 0 \\ {25} \\ \end{array}} \right) = - \left( {\begin{array}{*{20}c} {20\cos 70} \\ { - 20\sin 70} \\ \end{array}} \right) + \overrightarrow {OW} \\ \overrightarrow {OW} = \left( {\begin{array}{*{20}c} {20\cos 70} \\ {25 - 20\sin 70} \\ \end{array}} \right) \\ \end{array}$$

I then found the answer to be 9.24km/h on a bearing of 48 degrees, but the answer says 9.24hm/h on a bearing of 228 degrees. Have i gone wrong somewhere? is the book wrong? any help is greatly appreciated.

Thanks,
Dan.

2. Aug 7, 2006

### danago

Ok thanks to anyone who read this and would have helped, but i seem to have solved my own problem :P The answer gave the velocity of the wind coming FROM 228 degrees. The answer i obtained was the wind going TO a direction of 48 degrees.

Guess id better learn to read properly :P

3. Aug 7, 2006

### meee

oh yay good job 10chars