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 1.00 m to the North then she turns West and walks 11.3 m. Lastly she decides to be adventurous and walk 8.80 m at 48.0 degree South of East. (Use East as positive x and North as positive 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 = 1 j m

So Ax = 0, Ay = 1 m

B = - 11.3 i  m

So Bx = -11.3 m , By = 0

C = 8.80 cos48 i - 8.80 sin48 j

   = 5.88 i - 6.539 j m

So Cx = 5.88 m , Cy = -6.539 m

Resultant displacement R = A + B + C

                                      = 1 j - 11.3 i + 5.88 i - 6.539 j

                                      = - 5.42 i - 5.539 j   m

So Rx = -5.42 m , Ry = -5.539 m

Magnitude of R = Sqrt[(-5.42)^2 + (-5.539)^2]

                       = Sqrt[60.05]

                       = 7.749 m

Angle made by Resultant vector R with +ve X axis = Tan^-1[5.539/5.42] + 180

                                                                             = 45.62 + 180 = 225.62 degrees

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