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:

Drawing the path of the van we get a shape with two exposed points A and E. If we draw a line from point E perpendicular to AC we get point B. This gives us a right angled triangle AEB.

From Pythagoras theorem

AE² = AB² + EB²

`AE=√(AB^2+EB^2)\\\Rightarrow AE=√(2^2+4^2)\\\Rightarrow AE=√(20)\\\Rightarrow AE=4.47\ km`

Hence, the van is 4.47 km from its initial point