Homework Help: 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