A) Write an expression for the x-component of the final displacement in terms of

Question

A) Write an expression for the x-component of the final displacement in terms of the given quantities.

B) Write an expression for the y-component of the final displacement in terms of the given quantities.

C) What is the magnitude of my displacement vector (in meters) as measured from the origin?

D) What is the angle of my displacement vector as measured counterclockwise from the +x-axis?

(10%) Problem! 3:1 start walking. The lst leg of my trip I walk dA-145 m at a-12° south of east. The 2nd leg of my trip I walk dB 105 m at 29 north of east. On my final leg I walk dc-85 mat 63 north of west. Choose the coordinate system so that x is directed towards the east, and y is directed towards the north.

Explanation / Answer

A)

X - component of final displacement

Dx = dAcosA +dBcosB -dCcosC

DX = 145cos12 + 105cos29 - 85cos63

DX = 195.1 m

B)

Y - component of final displacement

DY = -dAsinA +dBsinB + dCsinC

DY = -145sin12 + 105sin29 + 85sin63

DY = 96.5 m

C)

Magnitude of total displacemt

D = (DX2+Dy2)

D= (195.12 + 96.52)

D = 217.7 m

D)

Direction

= arctan(DY/DX)

= arctan(96.5/195.1)

= 26.32o

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