I the following problem,
A boat sails for one hour at 4km/h on a steady compass heading of 40º east of north. The boat is simultaneosly carried along by the current. At the end of the hour, the boat is 6.12km from its starting point. The line from its starting point to its locations lies 60º east of north. Find the easterly and northerly components of the waters velocity.
I know that:
4cos40 + c1 = 6.12cos60
4sin40 + c2 = 6.12sin60
My problems in understanding the solution is:
1 - Having a vector that starts from the origin and ends at 4cos40 and 4sin40.
Why 4cos40 gives the x axis position of the vector and 4sin40 give the y axis position of the vector? Is there a geometry explanation about that? I don't understands how this count represents the x and y position.
2 - The lenght of a vector multiplied by the cos of an angle gives always the x position? The same for the y position.