A4070 km at 165

degrees

B1600 km at 270

degrees

C2600 km at 340

degrees

A: 4070 km@165

B: 1600 km@270

C: 2600 km@340

HEAD TO TAIL- The Picture

RESULTANT

2000 km @ 240

Now we will complete the same problem using the “Goal Post Method” to solve the problem mathematically.

The picture from the “Head to tail” method will help guide us through the problem.

Remember:

•The Head to Tail method helps us estimate a resultant

•The “Goal Post Method” gives us a reliable value

A4070 km at 165

degrees

B1600 km at 270

degrees

C2600 km at 340

degrees

A: 4070 km@165

B: 1600 km@270

C: 2600 km@340

HEAD TO TAIL- The Picture

RESULTANT

? @ ?

Ay

Ax

Cy

Cx

By

Ay + By + Cy

Ax + Bx + Cx

Horizontal Component

X

Vertical Component

Y

4070km @165 4070 (cos 165)

-3931.3

4070 (sin 165)

1053.4

1600km @270 1600 (cos 270)

0

1600 (sin 270)

-1600

2600km@ 340 2600 (cos 340)

2443.2

2600 (sin 340)

-889.25

Totals -1488.1 -1435.85

To find the magnitude of the resultant use Pythagorean Theorem:

Resultant 2= (sum of x)2 + (sum of y)2

To find the direction of the resultant use inverse tangent:

Tangent -1 y/x = angle in quadrant

Resultant 2= (-1488)2 + (-1435)2

R = 2067 km

Angle = 46 degrees below west or 180 + 46

Angle = 226 degrees