Final answer:
The magnitude of displacement for a car that travels 20 km west and then 20 km south is approximately 28.3 km, calculated using the Pythagorean theorem.
Step-by-step explanation:
The magnitude of displacement for a car that travels 20 km west and then 20 km south can be determined using the Pythagorean theorem. Displacement is a vector quantity that represents the shortest distance between the starting point and the ending point, along with its direction. In this case, the car's movements form a right-angled triangle with the legs being the distances traveled west and south. Therefore, the magnitude of the displacement (R) is the hypotenuse of the triangle.
To calculate this:
- Recognize that you have a right-angled triangle where the two sides are 20 km each.
- Use the Pythagorean theorem which states that R2 = a2 + b2, where a and b are the legs of the triangle and R is the hypotenuse (displacement).
- Calculate by plugging in the values: R2 = 202 + 202
- Compute the sum: R2 = 400 + 400
- Calculate the square root of the sum: R = √800
- The result is R ≈ 28.3 km, which is the magnitude of the displacement.
Thus, the car's displacement magnitude is approximately 28.3 km.