EPHYS Chapter 3 Study Notes

EPHYS Chapter 3: Vectors

1. Vector Components in the xy Plane

  • Problem 1: What are (a) the x component and (b) the y component of a vector?
    • Direction: 250° counterclockwise from the positive direction of the x axis
    • Magnitude: 7.3 m
    • Answer:
    • (a) x component: -2.5 m
    • (b) y component: -6.86 m

2. Displacement Vector Calculation

  • Problem 2: A displacement vector in the xy plane is 15 m long and directed at an angle of 30°.
    • Calculate:
    • (a) x component
    • (b) y component
    • Answer:
    • (a) x component: 13 m
    • (b) y component: 7.5 m
  • Referenced Figure: Fig. 3-26

3. Magnitude and Direction from Components

  • Problem 3: Given the x and y components of a vector, determine:
    • Components:
    • x component: 25.0 m
    • y component: 40.0 m
    • Calculate:
    • (a) Magnitude of vector
    • (b) Angle between vector direction and the positive x direction
    • Answer:
    • (a) Magnitude: 47.2 m
    • (b) Angle: 122°

4. Angular Conversions

  • Problem 4: Express the following angles:
    • (a) 20.0° in radians
      gor (b) 50.0° in radians
    • (c) 100° in radians
      gor (d) Convert the following to degrees:
    • (e) 0.330 rad
      gor (f) 2.10 rad
    • (g) 7.70 rad
  • Answer:
    • (a) 0.349 rad
    • (b) 0.873 rad
    • (c) 1.75 rad
    • (d) 18.9°
    • (e) 120°
    • (f) 441°

5. Navigation Problem - Ship Route

  • Problem 5: A ship sails to a point 120 km due north but is blown by a storm to a point 100 km due east. Calculate:
    • (a) How far must it sail to reach its original destination
    • (b) What direction should it sail?
    • Answer:
    • (a) 156 km
    • (b) 129.8°

6. Walking Pattern Calculation

  • Problem 6: A person walks as follows:
    • 3.1 km north
    • 2.4 km west
    • 5.2 km south
  • Calculate:
    • (a) How far would a bird fly straight from start to finish?
    • (b) What direction?
    • Answer:
    • (a) 3.2 km
    • (b) 221°

7. Vector Addition and Calculation

  • Problem 7: Given two vectors:
    • Vector a:
    • a = (4.0 m)i - (3.0 m)j + (1.0 m)k
    • Vector b:
    • b = (-1.0 m)i + (1.0 m)j + (4.0 m)k
  • Calculate:
    • (a) a + b
    • (b) -5
    • (c) A third vector such that a - 6 + 7 - 0
  • Answer Detail:
    • For (a): a + b results in complex vector forms. Reference specific results documented later based on provided vector norms.
    • For (b): Detailed calculations leading to vector formulations.

8. Car Navigation Problem

  • Problem 9: A car drives:
    • 50 km east
    • 30 km north
    • Then in direction 30° east of north for 25 km.
  • Tasks:
    • (a) Sketch a vector diagram
    • (b) Determine:
    • Magnitude of total displacement
    • Angle from the starting point
    • Answer:
    • Total displacement magnitude: 81 km

9. Minimum Travel Distance

  • Problem 10: A person must reach a point 3.40 km away at 35.0° north of east, constrained to travel along streets. Find the minimum distance.
  • Answer: Minimum distance: 4.74 km

10. Survey Method for River Width

  • Problem 11: A surveyor measures distance across a river:
    • Walks 100 m along the bank to establish a line
    • Angles at 35.0° to a tree on the opposite bank.
  • Calculate the river's width.
  • Answer: The width of the river: 70 m

11. Vector Magnitude Condition

  • Problem 12: Vector A has a magnitude of 35.0 units, details missing in the transcript for completion.