A delivery truck travels 20 blocks north, 15 blocks east and 18 blocks south. What is its final displacement from the origin? Assume the blocks are equal length.
20 north and 15 south leaves 2 north
so, final displacement is 2 north, 15 east.
To find the final displacement of the delivery truck from the origin, we need to calculate the net displacement in both the north-south and east-west directions separately.
Let's start with the north-south direction. The truck initially travels 20 blocks north and then 18 blocks south. Since the truck ends up 18 blocks south, we need to subtract its southward displacement from its northward displacement. So, the net displacement in the north-south direction is 20 blocks - 18 blocks = 2 blocks north.
Now let's consider the east-west direction. The truck travels 15 blocks east, which means its displacement in the east direction is 15 blocks.
Since displacement is a vector quantity, to find the final displacement, we need to combine the north-south and east-west displacements using vector addition. We can imagine these displacements as the two legs of a right-angled triangle, and the final displacement as the hypotenuse.
Using the Pythagorean theorem, we can calculate the magnitude of the final displacement:
Magnitude of displacement = √(2² + 15²) = √4 + 225 = √229 ≈ 15.13 blocks
Therefore, the truck's final displacement from the origin is approximately 15.13 blocks.