Figure 1 Coordinate system


The addition of vectors by the component method



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2-Vector

The addition of vectors by the component method





  1. Figure 2.34



    Figure 2.35
    A hiker moves 5 km west and 12 km south. Find the magnitude and direction of the resultant displacement. (13 km S-W).

  2. 25 km due east, then 40 km due north. Find the resultant of displacements.

  3. We are given Rx = 3.00 m and Ry = 4.00 m, as shown in Figure 2.34. Find the resultant vector R and an angle.

  4. Resultant vector is equal to R = 13 m. If x-component of resultant vector is 5 m. What angle does resultant vector make with horizontal?

  5. Resultant vector makes an angle with vertical axis and its magnitude is 35 m. If x-component of the resultant vector is equal to 4 m. Find the angle.

  6. Given two vectors and as shown in Figure 2.35. The magnitude of each vector is A = 5 m, B = 9 m. By using components of the vectors find the magnitude and direction if add vectors and if we subtract vectors .




  7. Figure 2.36



    Figure 2.37
    A hiker walks 30 km from a camp on a course of 35° west of north. Another day he walks 40 km due west. Last day he travels 72 km on a course of 25.0° east of south. Find the displacement from the starting point to the ending point, Figure 2.36.

  8. A ship starts from port and takes the route shown in Figure 2.37. The ship first travels to an island A, located 100 km away on a course of 300 north of east. Then it travels for 80 km 200 west of north, to a second island, B. Then it travels 120 km due west, to a third island, C. Find the displacement from the starting point to the ending point.

  9. A ship travels and moved 55 km due north, then it traveled 75 km at 25° north of east, and finally it traveled 70 km at 45° north of west. Find the resultant of displacements of the ship and the angle of displacement.

  10. A car moved 90 km at 40° north of east, then it traveled 150 km at 35°east of south, and at the end the car passed 120 km at 25° north of east. Find the resultant of displacements and direction.

  11. A plane moved 380 km due south, then 470 km at 20° north of east, and then it landed by traveling 430 km at 30° south of east. Find the resultant displacements and the angle resultant displacement made.

  12. SUV passed 1000 km at 15° north of east, then it covered 800 km at 30° east of south, and then it stopped after traveling 550 km at 20° west of south. What is the resultant displacement? Find the angle of resultant displacement.

  13. A truck moved 90 km at 25° west of north, then it passed 75 km at 35° east of north, and then finally 65 km due east. Determine resultant vector displacement and direction.

  14. At the beginning travelled distance of an air balloon is 55 mi at 40° north of east, then it covered 70 mi at 55° north of east, then it’s direction of motion is 45 mi at 25° north of east, and then finally it moved 40 mi at 15° north of east.

  15. We are given traveled distances of a ship as follows: 10 mi at 30° west of south, then 20 mi at 40° north of east, then 30 mi at 10° north of east, and then 15 mi at 25° west of north. What is the resultant displacement and direction of the ship?

  16. Find the resultant of the following three displacements; 3 mi due east, 6 mi east-northeast, and 7 mi northwest.

  17. A pedestrian moves 200 m horizontally and then rises 135 m at an angle of 300 above the horizontal. Next, it travels 135m at an angle of 40.0 below the horizontal. Find displacement from its starting point to the end of this movement.




  18. Figure 2.38



    Figure 2.39
    A plane flies 150 km due east from airport A to airport B and then 200 km in the direction of 300 north of east from airport B to airport C. (a) Find displacement between airport A and airport C? (b) In what direction is airport C with respect to airport A?

  19. A plane starts from airport and flies 65 km 400 north of west and then it flies 90 km at 30.00 north of east. Find the plane’s displacement and direction.

  20. A sled moving across a floor travels through two displacements. The first displacement is 200 cm and makes an angle of 600 north of west. The resultant displacement is 190 cm and is directed at 400 north of east. Find the magnitude and direction of the second displacement.


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