Calculating the Vector Displacement of Steve's Car
Steve's Car Errands
Steve is driving in his car to take care of some errands. The first errand has him driving to a location 2 km East and 6 km North of his starting location. Once he completes that errand, he drives to the second one which is 4 km East and 2 km South of the first errand.
Calculating the Magnitude of the Vector
What is the magnitude of the vector that describes how far the car has traveled from its starting point, rounded to the nearest km?
Question
What is the magnitude of the vector that describes how far the car has traveled from its starting point, rounded to the nearest km?
Final answer:
The magnitude of the displacement vector for Steve's car from its starting point after his errands is approximately 7 km when rounded to the nearest km.
Explanation:
Steve is looking to calculate the magnitude of the vector from his starting point after completing two errands. Initially, he travels 2 km East and 6 km North, then 4 km East and 2 km South for his subsequent errands. To determine the total displacement from the starting point, we find the resultant vector in the east and north directions.
For the eastward displacement, add the east components: 2 km + 4 km = 6 km East. For the northward displacement, subtract the southward movement from the northward movement: 6 km - 2 km = 4 km North. The total displacement vector is therefore 6 km East and 4 km North.
To find the magnitude of this resultant vector, we use the Pythagorean theorem: magnitude = √(6^2 + 4^2) = √(36 + 16) = √52 ≈ 7.2 km.
Rounding to the nearest km, the magnitude of the vector that describes how far Steve's car has traveled from its starting point is approximately 7 km.