Question

A man walks 600 m [E47°N], then 500 m [N38°W], then 300 m [W29°S], and finally 400 m [S13°E]. Find his resultant displacement.

Answer 1

The horizontal component of an angular distance can be calculated by multiplying the distance with the cosine of the angle, Dx = D * cos θ

While the vertical component is calculated by multiplying the distance with the sine of the angle, Dy = D * sin θ

The resultant displacement can then be obtained using the formula for hypotenuse and summations of each component:

R^2 = (summation of Dx)^2 + (summation of Dy)^2

summation of Dx = 600 * cos47 + 500 * cos128 + 300 * cos209 + 400 * cos(-77) = -71.0372

summation of Dy = 600 * sin47 + 500 * sin128 + 300 * sin209 + 400 * sin(-77) = 297.6267

                        Note: you have to draw the lines to correctly determine the angles

R^2 = (-71.0372)^2 + 297.6267^2

R = 306 m

The resultant angle is:

tan θ = Dy / Dx

θ = tan^-1 (297.6267 / -71.0372)

θ = 103˚ = [N 13˚ W]

Therefore displacement is 306 m [N 13˚ W].