(7%) Problem 12: Suppose you first walk 12 m in a direction 20° west of north an

Question

(7%) Problem 12: Suppose you first walk 12 m in a direction 20° west of north and hen 24.5 m in a direction 40° south of west as shown in the figure. 400 20° Otheexpertta.com 25% Part (a) what is the component of your displacement in the x-direction, in meters? 25% Part (b) What is the component of your displacement in the y-direction, in meters? 25% Part (c) How far are you from your starting point in meters? 25% Part (d) What is the angle of a line connecting your starting position to your final position, measured South of West, in degrees? Grade Summary Deductions 0% Potential 100%

Explanation / Answer

First of all, resolve the components of vector A and B.

(a) In x direction, (be aware of the direction when writing components)

Dx = Ax + Bx

Dx = -12*sin20 - 24.5*cos 40

Dx = - 4.10424 - 18.768

Dx = - 22.87224 m

(b) In y direction

Dy = Ay + By

Dy = 12*cos 20 - 24.5 sin 40

Dy = 11.2763 - 15.748

Dy = - 4.4717 m

(c) D = sqrt ( Dx2 + Dy2)

D = sqrt ((- 22.87224)2 + (- 4.4717)2)

D = 23.305 m

(d) direction = tan-1 (4.4717 / 22.87224)

direction = 11.0620

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