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

1. A hiker walked 3.0 km [E] then 5.0 km [N]. What was the hiker's displacement?
2. A shopper in the downtown area walked 2 blocks north, 1 block west, 3 blocks south, and 3 blocks east. What was the shopper's displacement from where he started?
3. A hiker walked 3.0 km [E] then 5.0 km [N20ºE]. What was the hiker's displacement?
4. Two children pulled on a wagon by means of separate ropes. One child pulled with 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 wagon?

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

6. A small map shows Atlanta to be 730 miles in a direction 5.0º north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21º west of north from Atlanta. Assume a flat Earth and use
this information to find the displacement from Dallas to Chicago (in miles).

7. A jogger runs 100 m due west, then changes direction for the second leg of the run. 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 (north of west) and length of her second displacement?

8. A quarterback takes the ball from the line of scrimmage, runs backwards for 5.0 yards, then runs sideways parallel to the line of scrimmage for 17.0 yards. At this point, he throws a 50.0 yard forward pass straight down field, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

9.

If |d₁ + d₂| = |d₁ - d₂| for any two vectors, d₁ and d₂ (with different magnitudes and different directions), find the angle between d₁ and 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. A golfer takes three putts to get her ball into the hole once she is on the green. Her first putt displaces the ball 61.0 ft north; the second, 6.0 ft, 45 degrees south of east; and the third, 3.0 ft, 45 degrees south of west. What is the magnitude of the displacement (in feet) that would have been needed to get the ball into the hole on the first putt?

12. A sailboat tacking against the wind moves as follows: 5.8 km at 45º east of north, and then 4.5 km at 50º west of north. The entire motion takes 1 h 15 min 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 the skipper should steer to intercept the target in 2 hours.

14. A dog walks 0.64km due north, then runs due west . If the magnitude of the dog's displacement vector is 0.91km, what is the magnitude of the dog's displacement vector in the due west direction?

15.

a. What is the magnitude of the displacement of a car that travels half a lap along a circle that has a radius of 150m?

b. How about when the car travels a full lap?

ANSWERS

For solutions to all the problems on this page click here.

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'

For solutions to all the problems on this page click here.