Kinematics in Two Dimensions Summary

Motion in Two Dimensions

Key Concepts

  • Definition of Two-Dimensional Motion: Motion that occurs in both horizontal and vertical planes.
  • Compass Rose: Tool for expressing directions, e.g. [E 20° N] or [N 70° E].
  • Displacement Vectors: Can be added using scale diagrams for total displacement in two dimensions.

Learning Goals

  1. Objects movement analysis on horizontal and vertical planes.
  2. Expressing directions using the compass rose.
  3. Adding displacement vectors to find total displacement.

Success Criteria

  • Ability to move objects in two dimensions.
  • Express directions using compass rose effectively.
  • Apply scale diagrams for displacement.

Displacement Calculation Examples

  • Taxi moves 300 m [S], then 180 m [E]. Find resultant displacement.
  • A boy walks 1.7 km [E] and 1.2 km [S] to a skating arena; total resultant displacement is 2.1 km [35° S of E].

Velocity Components

  • To find north and east components of a car moving at 100 km/h [25° N of E]:
    • Use trigonometric functions based on angle.

Average Velocity

  • Average velocity formula: ( V_{avg} = \frac{Displacement}{Time} )
  • In multi-displacement cases, use the resultant displacement for the calculation.

Practical Problems

  1. Calculate total displacement of various movements using vector diagrams.
  2. Example questions involve running scenarios, boat crossing, and vehicle acceleration issues.

Special Cases

  • For circular motion (e.g., running around a track), average speed is calculated but average velocity may be zero due to no net displacement.
  • River crossing involves perpendicular motion calculations. Account for river current when determining the boat's resultant velocity and downstream distance.

Tips

  • Use vector diagrams to visualize movements and keeping track of directional changes.
  • Understand how to convert problem scenarios into vector format for easier calculations.