A delivery truck travels 10 km north, 18 km east, and 29 km south. What is its final displacement (in km) from the origin?
18km east, 19km south
distance= sqrt (18^2+19^2)
1 km South East
To find the final displacement of the delivery truck from the origin, we need to consider the net or overall movement of the truck.
Step 1: Represent the movements graphically
First, let's represent the movements on a Cartesian coordinate system. Assume the starting point (the origin) is (0,0).
The truck first travels 10 km north, which means it moves up along the y-axis by 10 units. So its position becomes (0,10).
Next, the truck travels 18 km east, which means it moves right along the x-axis by 18 units. So its position becomes (18,10).
Finally, the truck travels 29 km south, which means it moves down along the y-axis by 29 units. So its position becomes (18,-19).
Step 2: Calculate the displacement
To calculate the displacement, we find the straight-line distance between the final position of the truck and the origin.
Using the distance formula:
Displacement = √((x2 - x1)² + (y2 - y1)²)
Here, (x2,y2) = (18,-19) and (x1,y1) = (0,0).
Substituting the values:
Displacement = √((18 - 0)² + (-19 - 0)²)
= √(18² + (-19)²)
= √(324 + 361)
= √685
≈ 26.19 km
Therefore, the final displacement of the delivery truck from the origin is approximately 26.19 km.