A displacement vector points in a direction of theta = 27 degree left of the pos

Question

A displacement vector points in a direction of theta = 27 degree left of the positive y axis. The magnitude of this vector is D = 150 m. Part (a) Write expression for the x component vector, D_x, in terms of D, theta and the unit vectors i and j. Part (b) Write an expression for the y component vector, D_y, in terms of D, theta, and the unit vectors i and j. Part (c) Express the vector D in terms of D in terms of D, theta, and the unit vectors i and j. Part (d) What is the sum of the magnitudes of vectors D_x and D_y in meters?

Explanation / Answer

a)Dx/D = sin(theta)

Dx = - D sin(theta)i

b)Dy/D = cos(theta)

Dy = D cos(theta)j

c)D = D [sin(theta)i + cos(theta)j]

d)Dx = D sin(theta) = 150 x sin27 = 68.09 m

Dy = D cos(theta) = 150 x cos27 = 133.65 m

Hence, Dx = 68.09 m and Dy = 133.65 m

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