In this problem, you will add the three vectors together to get a resultant vect

Question

In this problem, you will add the three vectors together to get a resultant vector. A student is out walking in New York. She walks 3.20 m to the North then she turns West and walks 6.70 m. Lastly she decides to be adventurous and walk 15.0 m at 61.0 degree South of East. (Use East as positive x and North as postive y) What are the x and y components of vector A her first displacement? What are the x and y components of vector B, her next displacement? What are the x and y components of vector C, her last displacement?What are the x and y components of the resultant vector, her total displacement? What is the magnitude of the resultant vector?What is the angle of the resultant vector with respect to the positive x axis?

Explanation / Answer

A = 3.20 j   ; Ax = 0    ; Ay = 3.20 m

B = -6.70 i ; Bx = -6.70 m    ; By = 0

C = 15 cos 61o i - 15 sin 61o j = 7.27 i - 13.12 j

Cx = 7.27 m ; Cy = -13.12m

R = A + B + C = 3.20 j - 6.70 i + 7.27 i - 13.12 j = 0.57 i - 9.92 j

Rx = 0.57m     ;   Ry = -9.92m

R = (Rx2 + Ry2) = 9.936 m

= tan-1(Ry/Rx) = -86.71o ( CW with positif x axis )

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