The compass in a light aircraft shows that it is flying due north. The air speed indicator gives a reading of 150km/h. If there is a 50km/h wind blowing from west to east, what is the ground speed of the aircraft?

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- Jul 18th 2006, 12:49 PMbobby77please help
The compass in a light aircraft shows that it is flying due north. The air speed indicator gives a reading of 150km/h. If there is a 50km/h wind blowing from west to east, what is the ground speed of the aircraft?

- Jul 18th 2006, 02:40 PMQuickQuote:

Originally Posted by**bobby77**

use pythagorean theorum...

$\displaystyle c=\sqrt{150^2+50^2}$

$\displaystyle c=\sqrt{22500+2500}$

$\displaystyle c=\sqrt{25000}$

$\displaystyle c=50\sqrt{10}\approx158.114$ - Jul 18th 2006, 07:57 PMmalaygoel
It is always good to specify direction.

Direction will be $\displaystyle tan^{-1}(\frac{1}{3})$east of north.

Malay - Jul 18th 2006, 08:01 PMQuickA question by itself
I'm just learning vectors mind you...

would the velocity of the ground speed of the aircraft be $\displaystyle 50\bold{i}+150\bold{j}+0\bold{k}$ or $\displaystyle 50\bold{i}+0\bold{j}+150\bold{k}$? - Jul 18th 2006, 08:17 PMmalaygoelQuote:

Originally Posted by**Quick**

Draw a horizontal line and a line perpendicular to it(it will be obviously vertical).Label horizontal as x , vertical as y. Then z will be upwards out of the plane of the paper.

In the question

velocity of plane (without air)=0i+150j+0k

velocity of air=50i+0j+0k

resultant velocity=50i+150j+0k

(Actually there is a method which could tell you that the cordinate system used by you is acc. to international convention or not(based on cross product of vectors))