How can the wind speed and plane speed be calculated based on given information?

[P11maf]

First time posting hi guys and thanks for the help before i even start :)

here goes, i am on question 4 and I am not the best with this but to be far i am not 100% sure on the question here goes

An aircraft flies through still air at a velocity of 100ms-1 due East. However due to a wind blowing from the North it is found to be heading 15*(thats ment to be a little o but i can't remember how to do it on the computer) South of East. Calculate the wind speed and the speed of the plane relative to the ground. (27 ms-1, 104 ms-1)


i understand that that's the answer but how do i get it, I've no clue and to be far these questions have been doing my head in all day i can't understand it and I've to have it handed in by tomorrow i know i'll love all the help i can get thanks :D

 

[cristo]

Try drawing a diagram to start with. You have the plane's speed due east, and are told the angle south of due east that it actually heads on. You need to work out the speed of the wind (which is blowing due south) and the speed that the plane appears to be flying at (i.e the hypotenuese of the triangle).

[Hint: Use trigonometry]

 

[P11maf]

yeah but that's my problem i don't know how to do that, I've a few other drawings here but they really don't show me how to make my own that's why I am searching for help :|

 

[cristo]

Ok, well pick an origin.
1. "An aircraft flies due east" tells us that we must draw a line due east from the origin.
2. "It is found to be heading 15 degrees south of east" tells us that we must draw another line from the origin, at an angle 15 degrees south from east.
3. "The wind is blowing due south" tells us that we can join the right end of the horizontal line to the right end of the line at an angle of 15 degrees with a vertical line.

Now, write onto the diagram what you know. You should now be able to solve it.