On her trip from home to school, Karla drives along three streets after exiting the driveway. She drives 1.85 miles south, 2.43 miles east and 0.35 miles north. Determine the magnitude of Karla's resultant displacement. explanation on answer please
final location is 1.5mi south and 2.43mi east.
Now just use the Pythagorean Theorem to find the magnitude (the hypotenuse).
Velar
To determine the magnitude of Karla's resultant displacement, we need to find the net displacement from her starting point to her ending point.
Let's break down the given distances into their components:
1. The distance Karla drives 1.85 miles south. Since this is in the south direction, we can assign a negative value to this displacement: -1.85 miles south.
2. The distance Karla drives 2.43 miles east. This is in the east direction, so it remains positive: +2.43 miles east.
3. The distance Karla drives 0.35 miles north. Since this is in the north direction, it also remains positive: +0.35 miles north.
Now, let's add up these displacements:
-1.85 miles south + 2.43 miles east + 0.35 miles north = -1.85 + 2.43 + 0.35 = 0.93 miles
The magnitude of Karla's resultant displacement is 0.93 miles.
To determine the magnitude of Karla's resultant displacement, we need to find the straight-line distance between her starting point and ending point.
First, let's break down Karla's journey into its component vectors:
1.85 miles south: This represents a displacement vector in the south direction. We can represent this as a vector with a magnitude of 1.85 miles and a direction of 180 degrees (or -90 degrees if you prefer).
2.43 miles east: This represents a displacement vector in the east direction. We can represent this as a vector with a magnitude of 2.43 miles and a direction of 90 degrees.
0.35 miles north: This represents a displacement vector in the north direction. We can represent this as a vector with a magnitude of 0.35 miles and a direction of 0 degrees (or 360 degrees).
To find the resultant displacement, we need to calculate the sum of these vectors. We can do this by adding the horizontal components (east and west) separately and the vertical components (north and south) separately.
Horizontal component:
The eastward displacement vector has a magnitude of 2.43 miles, and the westward displacement vector has a magnitude of 0 miles since there is no westward movement. Thus, the horizontal displacement is 2.43 miles.
Vertical component:
The northward displacement vector has a magnitude of 0.35 miles, and the southward displacement vector has a magnitude of 1.85 miles. The combined vertical displacement is 1.85 - 0.35 = 1.5 miles south.
Now, we have the horizontal displacement of 2.43 miles and the vertical displacement of 1.5 miles south. We can use these components to calculate the magnitude of the resultant displacement using the Pythagorean theorem:
Resultant displacement^2 = (horizontal displacement)^2 + (vertical displacement)^2
Resultant displacement^2 = (2.43 miles)^2 + (1.5 miles)^2
Resultant displacement^2 = 5.9049 miles^2 + 2.25 miles^2
Resultant displacement^2 = 8.1549 miles^2
Taking the square root of both sides, we find:
Resultant displacement ≈ 2.86 miles
Therefore, the magnitude of Karla's resultant displacement is approximately 2.86 miles.