A person walks one block north, two blocks west, and then two blocks northwest. The magnitude and direction of the resultant are
A) 4.2 blocks at an angle of 55° west of north.
B) 4.2 blocks at an angle of 35° west of north.
C) 5.0 blocks at an angle of 55° west of north.
D) 5.0 blocks at an angle of 35° west of north.

Question

Quizplus · Accepted Answer

The resultant displacement can be found using vector addition. The two blocks northwest can be decomposed into north and west components (each 1.41 blocks due to the 45° angle of northwest direction, using $\sqrt{2}$ for each leg of a 1:1 right triangle). Adding these to the initial movements (1 block north and 2 blocks west), we get a total of 2.41 blocks north and 3.41 blocks west. The magnitude of the resultant vector is $\sqrt{(2.41)^2 + (3.41)^2} \approx 4.2$ blocks. The direction, using the tangent function, is $\tan^{-1}(3.41/2.41) \approx 55°$ west of north.

A Person Walks One Block North, Two Blocks West, and Then