Question

I start walking. The 1st leg of my trip I walk dA = 55 m at θA = 15° south of east. The 2nd leg of my trip I walk dB = 120 m at θB = 21° north of east. On my final leg I walk dC = 75 m at θC = 56.5° north of west. Choose the coordinate system so that x is directed towards the east, and y is directed towards the north.

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?

Answer 1

This problem is based on vectors and components.

Here is a picture of vectors.

(a) d_x + 55 cos 15 + 120 cos 21 - 75 cos 56.5 = 0

d_x = -123.76 m

(b) d_y - 55 sin 15 + 120 sin 21 + 75 sin 56.5 = 0

d_y = - 91.31 m

(c) d = sqrt ( d_x² + d_y²)

d = 153.8 m

(d) direction = arctan ( - 91.31 / -123.76)

direction = 36.41 degree

from + x axis, direction = 216.41 degree