Question

1. challenge: a delivery truck travels 18 blocks north, 11 blocks east, and 12 blocks south. what is the distance traveled and displacement? assume all blocks are the same length.

Explanation:

Step1: Calculate the distance traveled

The distance traveled is the sum of the lengths of each part of the journey.
$d = 18 + 11+12$

Step2: Calculate the displacement in the north - south direction

Let north be the positive direction. The displacement in the north - south direction $y=18 - 12=6$ blocks (north). The displacement in the east - west direction $x = 11$ blocks (east).
Using the Pythagorean theorem for displacement $s=\sqrt{x^{2}+y^{2}}$
Substitute $x = 11$ and $y = 6$ into the formula: $s=\sqrt{11^{2}+6^{2}}=\sqrt{121 + 36}=\sqrt{157}$

Answer:

The distance traveled $d = 41$ blocks. The displacement $s=\sqrt{157}\approx12.5$ blocks.