Question

A driver drives 3.25 km north, then 4.75 km west, and then 1.5 km south. Find the magnitude and direction of the resultant displacement using the method of derivation.

a) Magnitude: 4.6 km, Direction: 38.66° North of West
b) Magnitude: 5.25 km, Direction: 48.66° South of West
c) Magnitude: 5.25 km, Direction: 41.34° North of West
d) Magnitude: 4.6 km, Direction: 51.34° South of West

Answer 1

To find the magnitude and direction of the resultant displacement, we can use the method of vector addition by representing each leg of the journey as a vector and adding them together. The correct answer is option a) Magnitude: 4.6 km, Direction: 38.66° North of West.

Step-by-step explanation:

To find the magnitude and direction of the resultant displacement, we can use the method of vector addition. We can represent the first leg of the journey (3.25 km north) as a vector pointing upwards, the second leg (4.75 km west) as a vector pointing to the left, and the third leg (1.5 km south) as a vector pointing downwards. We can then add these vectors together to find the resultant displacement.

By using the Pythagorean theorem to find the magnitude of the resultant displacement and trigonometry to find the direction, we can determine that the correct answer is option a) Magnitude: 4.6 km, Direction: 38.66° North of West.