Question

1. a delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south. what is the distance traveled and displacement? assume all blocks are the same length.

Explanation:

Step1: Calculate the distance

Distance is the total path covered.
\(d = 18 + 10+16\) blocks
\(d=44\) blocks

Step2: Calculate the displacement

Let north - south be \(y -\) axis (\(+y\) for north and \(-y\) for south) and east - west be \(x -\) axis (\(+x\) for east).
The \(y -\) component of displacement: \(y=18 - 16=2\) blocks (north)
The \(x -\) component of displacement: \(x = 10\) blocks (east)
Using Pythagoras theorem for displacement \(s=\sqrt{x^{2}+y^{2}}\)
\(s=\sqrt{10^{2}+2^{2}}=\sqrt{100 + 4}=\sqrt{104}\approx 10.2\) blocks

Answer:

Distance: \(44\) blocks; Displacement: approximately \(10.2\) blocks