# Physics Help >> Index to Physics Homework Help » Vector Addition and Displacement Problems

## Problems

1. A hiker walked 3.0 km [E] then 5.0 km [N]. What was the hiker's displacement?
2. A hiker walked 2 blocks north, 1 block west, 3 blocks south, and 3 blocks east. What was the hiker's displacement?
3. A hiker walked 3.0 km [E] then 5.0 km [N20ºE]. What was the hiker's displacement?
4. Two children pulled on ropes attached to a cart: onewith a force of 200 N, and the other pulled with a force of 150 N. The two ropes formed an angle of 20º. What was the net force on the cart?

5. A bird flies 80.0 m east, then 100.0 m 50º south of east. What is the bird's displacement?

6. Three markers are on flat terrain. Marker A is 730 miles in a direction 5.0º north of east from Marker D, while Marker C is 560 miles 21º west of north from Marker A. What is the displacement from Marker D to Marker C?

7. A jogger runs west for 100 m, then changes direction. At the end of the run, she is 175 m away from the starting point at an angle of 15.0° north of west. What were the direction and length of second part of her run?

8. A football player runs backwards for 5.0 yards, then runs sideways parallel to the 50 yard line for 17.0 yards, then throws a 50.0 yard pass straight forward, perpendicular to the 50 yard line. What is the magnitude of the football's resultant displacement?

9.

Find the angle between d1 and d2 if |d1 + d2| = |d1 - d2|

10. A ship sailed 2.8 km north, then 3.5 km west and finally 10.1 km southwest.

a. Sketch a vector diagram representing this motion.

b. What is the net displacement of the ship?

11. An ant crawls 61.0 ft north; then, 6.0 ft, 45 degrees south of east; and finally, 3.0 ft, 45 degrees south of west. What is the magnitude of the displacement (in feet) that would have been needed to straignt to the final destination from where the ant started?

12. A boat travels 5.8 km at 45º east of north, and then 4.5 km at 50º west of north. What is the total displacement?

13. A target is 12000 meters away on a compass bearing of 30 degrees, moving on a heading of 140 degrees at a steady (4.1 m/s). Determine the course and speed required to intercept the target in 2 hours.

14. A kangaroo hops 0.64km north, then hops west . If the magnitude of the roo's displacement is 0.91km, how far did the roo travel in the west direction?

15. A car travels around a circle with a radius of 150 m.

a. What is the magnitude of the car's displacement at half a lap?

b. What is the magnitude of the car's displacement at a full lap?

11.

The net North component of the resultant displacement is

61 - 4.24 - 2.12 = 54.64' [N]

The net East component of the resultant displacement is

4.24 - 2.12 = 2.12' [E]

The magnitude of the resultant displacement is

d = √((54.64)2 + (2.12)2) = 54.68'