Lecture Notes: 2D Kinematic Equations

Introduction

• Focus on 2D kinematic equations.
• Use animation of a ball being kicked to illustrate concepts.
• Velocity has x and y components:
  • $v_x = v \cos \theta$
  • $v_y = v \sin \theta$
• 2D kinematics more realistic compared to 1D kinematics.

Review of 1D Kinematics

• Displacement: $\Delta x = x_f - x_i$ (final minus initial positions).
• Foundation for velocity, speed, and acceleration equations.

Transition to 2D Kinematics

• Position vectors originate from the origin and are represented as:
  • $x\hat{i} + y\hat{j}$ (unit vectors).
• Change in position vector: $\Delta \mathbf{r} = \mathbf{r}_f - \mathbf{r}_i$.
• Displacement in 2D: $\Delta x \hat{i} + \Delta y \hat{j}$.
• Average velocity in 2D: $\frac{\Delta x}{\Delta t} \hat{i} + \frac{\Delta y}{\Delta t} \hat{j}$.

Adapting 1D Equations to 2D

• Constant acceleration equations in 1D adapted to 2D:
  • $\Delta v_x = a_x t$
  • $\Delta v_y = a_y t$
  • Similar adaptations for other equations.

Problem-Solving Strategy for 2D Motion

• Treat x and y motion separately.
• Break vectors into components.
• Create specific equations for the problem.
• Identify important events based on time, location, or special points.

Organizing Problem-Solving

• Create a chart to organize information based on important events.
• Columns represent events; rows show known information:
  • Horizontal position, velocity, and acceleration.
  • Vertical position, velocity, and acceleration.

Summary & Tips

• Treat x and y motion independently.
• Identify important events and make a table of values.
• Use charts to organize and solve problems effectively.

Conclusion

• Overview of strategies for solving 2D kinematic problems.
• Encouragement to practice and apply these strategies.