Question

A moving van travels 10km North, then 4 km east, drops off some furniture and then drives 8 km south. (a) Sketch the path of the moving van. (2) How far is the van from its starting point? (Hint: it is the magnitude of the displacement vector).

Answer 1

4.47 km

Step-by-step explanation:

If we draw the path of the van then we get a shape with two exposed points A and D. If we draw a line from point D perpendicular to BA we get point E. This gives us a right angled triangle ADE.

From Pythagoras theorem

AD² = AE² + ED²

`AD=√(AE^2+ED^2)\\\Rightarrow AD=√(2^2+4^2)\\\Rightarrow AD=√(20)\\\Rightarrow AD=4.47\ km`

Hence, the van is 4.47 km from its initial point