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.
Displacement=sqrt{(20-18)^2 +15^2}=15.13 m
I like the 15.13, but where did you come up with meters? :-)
To find the final displacement from the origin, you need to calculate the net distance and direction traveled by the delivery truck.
1. Start by plotting the movements of the truck using a coordinate system. Assume the origin is at (0,0).
2. The truck travels 20 blocks north, so its new position would be (0,20).
3. Then, it travels 15 blocks east, resulting in a final position of (15,20).
4. Finally, it travels 18 blocks south, which means it moves down to (15,2).
5. The final displacement from the origin is the straight line distance from the origin to the final position of the truck.
6. Use the Pythagorean theorem to calculate the straight line distance:
- Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1,y1) is the origin (0,0), and (x2,y2) is the final position of the truck (15,2).
- Distance = √((15 - 0)^2 + (2 - 0)^2)
= √(15^2 + 2^2)
= √(225 + 4)
= √229
The final displacement from the origin is approximately √229 blocks.