A man has to travel 50 m due north, 40 m due east, and 20 m due south to reach a field from his house. Determine his displacement from the house to the field.

Step-by-step solution

Let the starting point be the origin (0,0) . Taking East along the positive x-axis and North along the positive y-axis, the individual displacements are: d ₁ = 50 j d ₂ = 40 i d ₃ = -20 j The net displacement vector is: D = d ₁ + d ₂ + d ₃ = 40 i + (50 - 20) j = 40 i + 30 j The magnitude of the displacement is: | D | = 40^2 + 30^2 = 1600 + 900 = 50 m The angle made with the East direction is: = y x = 30 40 = 3 4 = ⁻¹(3/4) North of East.