Lecture Notes: Projectile Motion and MATLAB Coding

Introduction

• Previous class covered projectile motion, solving initial problem from textbook.
• Today's focus: solving Problem 283 for projectile motion.

Problem 283 Overview

• Given: Projectile launched from point A with initial velocity of 120 m/s at 40 degrees.
• Objective: Determine slant distance S (impact point B) and time of flight.
• Additional Information: Angle 20 degrees, horizontal distance 800 m.

Governing Equations

• Equation: Derived last class
  • y = -g * x^2 / (V_0^2 * cos^2(θ)) + x * tan(θ) + y_0
• Set coordinate system: Cartesian (x, y) for simplicity.
  • Initial height y_0 is zero.
  • Total horizontal distance: x = 800 + S * cos(20°).
  • Vertical distance: y = S * sin(20°).*

Solution Strategy

1. Calculate S using MATLAB:
   • Use symbolic computation to solve for S.
   • Define constants and expressions.
   • Solve equation with MATLAB to find slant distance.
2. Calculate Time of Flight:
   • Use equation: x = V_0 * cos(θ) * t + x_0.
   • Simplified for initial x: t = x / (V_0 * cos(θ)).
   • Compute using values for total x and V_0.*

MATLAB Coding Overview

• Importance of MATLAB in engineering.
• Coding tips:
  • Use clc, clear, close all for clean workspace.
  • Define and solve equations using symbolic variables.
  • Convert angles to radians for computation.

Practical Application

• Discussed coding in MATLAB for real-world problems.
• Future use in ME520, ME530, and robotics (ME532).
• Emphasis on learning MATLAB and Python for engineering.

Additional Problem Example

• Basketball player shooting problem to illustrate initial angle determination using projectile motion.
• Set coordinate system with given conditions (height, distance).

Transition to Dynamics

• Normal and Tangential Coordinate System:
  • Used in dynamics for curved paths (e.g., car on a ramp).
  • Explanation of unit vectors and their properties.
  • Velocity in direction of tangential unit vector.
  • Acceleration components in normal and tangential directions.

Key Concepts

• Right-hand rule for determining directions.
• Understanding of angular velocity and acceleration.
• Importance of unit vectors and their derivatives in motion analysis.
• Application of dynamics principles to real-world engineering problems.

Conclusion

• Solved projectile problem using MATLAB.
• Introduced dynamics concepts for future learning.
• Emphasized importance of computational tools in engineering.

• Next Lecture Preview: Further exploration of dynamics systems and unit vector calculus.