Question

A team of biologists is tracking the motion of a mountain lion. The lion walks north for 880 meters, then turns and walks west for 1760 m. What is the displacement vector for the lion's motion?

Jonah is walking along a trail. The trail heads east for 1350 meters, before turning north and continuing for 990 meters. At the end of the trail, what is Jonah's displacement vector?
A metro train starts from a terminal station. The train heads north for 475 m, then west for 165 m, then north for 410 m, then east for 650 m where it arrives at the next station. What is the magnitude of the displacement vector from the terminal station to the next station?
Melinda is taking a tour through a new city. On the tour, she walks 0.40 miles south, 0.65 miles east, 0.78 miles north, 1.24 miles west, then 1.20 miles south. At the end of the tour, what is Melinda's displacement vector?
Terrence is surveying a plot of forest land. He walks 65 meters east, 210 meters south, 235 meters west, 115 meters south, 40 meters east, and 70 meters north. What is his displacement from the starting point?
Devon is designing the course for an upcoming race. The course he has designed runs 105 meters west, 605 meters south, 475 meters east, 915 meters south, 825 meters east, 1265 meters north, then 810 meters west. What is the displacement vector from the starting line to the finish line?
A particle is moving through an electric field. Starting from the origin, it first moves 7.22 cm in the negative y-direction, then it moves 8.05 cm in the positive x-direction. What is the direction of the resultant vector?
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?
Anja is driving west in a straight line. After driving for 5.50 km, she turns south and drives for 9.20 km. At the end of her drive, what is the magnitude of her displacement?
Terry walks 755 meters north, then turns and walks 425 meters west. What is the magnitude of Terry's displacement at the end of his walk?

Answer 1

The displacement vector is found by calculating the east-west and north-south components using trigonometry for each segment of the path and then summing these components to get the total displacement.

Step-by-step explanation:

The displacement vector represents the change in position of an object, taking into account only the initial and final positions and not the path taken. To calculate the displacement vector when given multiple movements with angles, we can use trigonometry to find the components of each displacement and then sum up these components to find the total displacement in the east-west (x-axis) and north-south (y-axis) directions.

For instance, if a person walks 25.0 m at an angle of 49.0° north of east, we can find the eastward and northward components of this displacement using the cosine and sine functions, respectively. Similarly, for the second displacement of 23.0 m at 15.0° north of east, and the third displacement of 32.0 m at 68.0° south of east, we can find their respective components.

Finally, we sum the eastward components to find the total displacement in the east-west direction and the northward components to find the total displacement in the north-south direction. The displacement vector can then be represented in component form or as a magnitude with direction.