# Vector question (relative speed)

• May 2nd 2009, 04:06 PM
Solid8Snake
Vector question (relative speed)
A plane goes from city A to city B. In a Cartesian plane, city A is at the origin and city B has coordinates (100,150). If there is no wind, the flight lasts one hour. Unfortunately, there is a wind. If the pilot does not adjust his flight path, he will be at point (120,160) after an hour. What is the speed of the wind?

I am having trouble doing this question, and my teacher has warned there will be a question similar to this on our test. I would like to know the steps I need to take in order to solve this question.
• May 2nd 2009, 06:06 PM
Soroban
Hello, Solid8Snake!

Quote:

A plane goes from city A to city B. In a Cartesian plane.
City A is at the origin and city B has coordinates (100,150).
If there is no wind, the flight lasts one hour. Unfortunately, there is a wind.
If the pilot does not adjust his flight path, he will be at point (120,160) after an hour.
What is the speed of the wind?

Code:

      |                            C       |                            o(120,160)       |                          * *       |                      *  *       |                    *    *       |                *      *       |              *        *       |          *          o(100,150)       |        *        *    B       |    *    *       |  *  *     A * - - - - - - - - - - - - - - - - - - -       |

The plane's original vector was: . $\overrightarrow{AB} \:=\:\langle100,150\rangle$

Due to the wind, $\overrightarrow{BC} \:=\:\langle x,y\rangle$, it flies to $C(120,160).$

Since $\overrightarrow{AB} + \overrightarrow{BC} \:=\:\overrightarrow{AC}$, we have: . $\langle 100,150\rangle + \langle x,y\rangle \:=\:\langle120,160\rangle$

. . Hence: . $\begin{array}{ccccccc}100 + x \:=\:120 & \Longrightarrow & x \:=\:20 \\ 150 + y \:=\:160 & \Longrightarrow & y \:=\:10 \end{array}$

The wind's vector is: . $\overrightarrow{BC} \:=\:\langle 20,10\rangle$

Its speed (magnitude) is: . $|\overrightarrow{BC}| \;=\;\sqrt{20^2+10^2} \;=\;\sqrt{500} \;=\;10\sqrt{5}$

• May 2nd 2009, 06:43 PM
Solid8Snake
thx a million