Question

ariane is riding her motorcycle, heading directly south. she drives south for 7.0 km, then turns west and drives west for 1.4 km. what is the direction of ariane's resultant displacement vector?

Answer 1

Ariane's resultant displacement vector points to the southwest direction.

Step-by-step explanation:

To find the direction of Ariane's resultant displacement vector, we can use the concept of vector addition. Ariane initially drives south for 7.0 km and then turns west and drives west for 1.4 km.

If we represent south as the negative y-direction and west as the negative x-direction, we can add these displacements vectorially. The vector representing the 7.0 km south displacement would be (0, -7.0) and the vector representing the 1.4 km west displacement would be (-1.4, 0). Adding these vectors gives us a resultant displacement vector of (-1.4, -7.0).

Therefore, Ariane's resultant displacement vector points to the southwest direction.

Answer 2

Ariane's resultant displacement vector direction is southwest, combining her southward and westward movements.

Step-by-step explanation:

Ariane's resultant displacement vector would be in a direction that is southwest of her starting point. To calculate this, we can consider her southward and westward movements as perpendicular components of her overall displacement. Using the Pythagorean theorem, we could calculate the magnitude of her displacement, but since the question only asks for the direction, this is not necessary. The direction is simply the combination of the two directions she has traveled: south and west. The graphical method for finding the direction of Ariane's displacement would involve drawing a straight line 7.0 km south and then a straight line 1.4 km westward from the end of the first line. The resultant displacement would be the vector from her starting point to the end of the second line, and its direction is southwest.