A delivery truck travels 19 blocks north, 14 blocks west and 15 blocks south. What is its final displacement from the origin?
19-15 = 4 north
14 west
sqrt (4^2 + 14^2) = sqrt(212) = 14.6
since its goes south after ward it is parrelel to north therefore you subtract 19 -15 which gives you 4 blocks since that s left over of 19 (u do this to make a triangle to find the displacement) and since 14 blocks is connecting the S and the N it is the ajacent of the triangle and 4 is the base so you do pythagorean theorm and that would be the diplacement. 4(squared)+ 14(squared)=c(squared)
To find the final displacement from the origin, we need to consider both the distance traveled and the direction traveled. Let's break down the problem step by step:
1. Start at the origin (0, 0) on a coordinate plane.
2. The truck travels 19 blocks north. Moving north on a coordinate plane means adding to the y-coordinate. So, we update the y-coordinate to 19.
3. The truck then travels 14 blocks west. Moving west on a coordinate plane means subtracting from the x-coordinate. So, we update the x-coordinate to -14.
4. Finally, the truck travels 15 blocks south. Moving south on a coordinate plane means subtracting from the y-coordinate. So, we update the y-coordinate to 19 - 15 = 4.
Now we have the final coordinates of the truck, which are (-14, 4). To find the displacement from the origin, we can use the distance formula:
Displacement = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the origin (0, 0) and the final coordinates of the truck (-14, 4), we get:
Displacement = √((-14 - 0)^2 + (4 - 0)^2)
= √((-14)^2 + 4^2)
= √(196 + 16)
= √212
≈ 14.56 (rounded to two decimal places)
Therefore, the final displacement of the delivery truck from the origin is approximately 14.56 blocks.