Question

A delivery truck travels 10 blocks north, 11 blocks east and 12 blocks south. What is its final displacement from the origin? Assume the blocks are equal length.
(a) Magnitude ?
. blocks
What's the Direction ?. ° (counterclockwise from east is positive)

Answer 1

Here is a basic drawing of the movement of the truck as the sum of three vectors:The individual displacement vectors are\[\overrightarrow{V_1}=10\overrightarrow{y}\]\[\overrightarrow{V_2}=11\overrightarrow{x}\]\[\overrightarrow{V_3}=-12\overrightarrow{y}\]The vectors can be summed directly as the sum of their respective components to give the components of the resultant displacement vector:\[\overrightarrow{d}=\overrightarrow{V_1}+\overrightarrow{V_3}+\overrightarrow{V_3}\]With this displacement vector in the form of its components you can now treat each component as the leg of a right triangle. The magnitude of the displacement can then be given by the Pythagorean theorem, and the angle can be found through an inverse trigonometric function.

Answer 2

Here is a basic drawing of the resulting displacement vector superimposed on coordinate axes, along with the angle, theta, noted: