SOLUTION: Hey, im stuck on a question, thanks for any help. The question is; When orineteering, Jack walks X km on a bearing of 100 (Degrees) from his starting point O, then walks Y km on

Question 106408This question is from textbook Mechanics I
: Hey, im stuck on a question, thanks for any help. The question is;
When orineteering, Jack walks X km on a bearing of 100 (Degrees) from his starting point O, then walks Y km on a bearing of 200 (Degrees) to a hut, H. Calculate the magnitude and direction of the displacement vector OH (arrow above facing right) when,
x = 6 and y = 7.
I've tried the sine and cosine rules, but all i can make out is two sides and no angles, i can't find another angle, i have no idea how to solve this problem, i have the answers also, i tried working backwards but still can't find the way, thanks for any help in advance! :D This question is from textbook Mechanics I

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Jack starting point,0, is the center of a circle and its radius is X km.
I'm assuming that 0 degrees is to the right (East if North is up).
You can re-orient the graph to change that if necessary (North is zero degrees,etc.).
When he changes direction (point A), imagine another center of a circle now with a radius of Y km.
You are trying to find the point H, on the second circle.
Set up a grid centered on 0 as (0,0).
When he travels X km on a bearing of 100 degrees, he travels (Xcos(100), Ysin(100)) on the grid.

A new circle is now centered at A.
He then changes direction and he walks an additional (Ycos(200),Ysin(200))

His total travel on the x axis is

His total travel on the y axis is

These are also the coordinates of H since you start at (0,0).

H coordinates are (-7.62,3.51)
The vector OH is therefore the vector from (0,0) to (-7.62,3.51)
Magnitude of OH is

Direction of OH is where

Hopefully these match your answers.
Good luck.
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