Question

Problem:

You found a treasure map!It said,start at the well,go 100m straightSouth,then 30m, 40 degrees North of West,then 25m straight East,and finally,45m,75 degrees South of East.Using BOTH polygon/parallelogramand component method of vector addition,how far from the well and in what direction is the hidden treasure?

Solution:

Graphical Method:Parallelogram/Polygon

Scale:

Final Answer:

Solution:

Analytical:Component Method

Final Answer:

Answer 1

Graphical Method: 120 m @ 8° E of S / 110 m @ 5° E of S.

Analytical (Component) Method assuming +x is in E direction and +y is in N direction

:

$$D_{1x}=0,\\D_{1y}=-100.\\ D_{2x}=-30\cos40°=-23, \\D_{2y}=30\sin40=19.3.\\ D_{3x}=25, \\D_{3y}=0.\\ D_{4x}=45\cos75°=11.6,\\D_{4y}=-45\sin75°=-43.5.\\ D_x=\Sigma D_{ix}=13.6,\\ D_y=\Sigma D_{iy}=-124.\\ D=\sqrt{D_x^2+D_y^2}=125\text{ m},\\\theta =\arctan\frac{D_y}{D_x} =6.25°\text{ E of S}.$$