Question

7. A man walks 4km North, then 3 km East and then 4 km South. Find the displacement from the starting point?
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Answer 1

Using i and j as the unit vectors in the x- and y-directions, and taking east to be the x-direction, then the boy’s final position is

r = 4i + 3j

The magnitude of this vector is √(4^2 + 3^2) = 5

The angle of the boy is Tan^-1(4/3) = 53.13° east of north

So the boy’s final position is 5km from the starting point, 53.13° east of north.

Of course, we all recognized that it was a 3–4–5 triangle, but I used the vector approach (which is the correct approach) to demonstrate the method.