a car travels 3.0km due south and then4.0km west what is lt's displacememt from the starting point

To calculate the displacement of the car from its starting point, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the car travels 3.0 km due south and 4.0 km west, forming a right-angled triangle. We can consider the south direction as the negative y-axis and the west direction as the negative x-axis.

The displacement can be represented by a vector in terms of its horizontal (x) and vertical (y) components, where the x-component represents its westward displacement and the y-component represents its southward displacement.

The horizontal displacement (x) is -4.0 km (westward) because it's in the opposite direction of the positive x-axis.

The vertical displacement (y) is -3.0 km (southward) because it's in the opposite direction of the positive y-axis.

Using the Pythagorean theorem:

Displacement^2 = (x)^2 + (y)^2
Displacement^2 = (-4.0 km)^2 + (-3.0 km)^2
Displacement^2 = 16.0 km^2 + 9.0 km^2
Displacement^2 = 25.0 km^2

Taking the square root of both sides:

Displacement = √(25.0 km^2)
Displacement ≈ 5.0 km

Therefore, the displacement of the car from its starting point is approximately 5.0 km.