SUMMARY
The discussion centers on solving for T in the horizontal projectile motion equation, specifically the equation 0 = Vi / K (1 - e^-kt)(sin theta) + (g / k^2)(1-kt-e^-kt). Participants highlight the complexity of the equation due to the presence of T both inside and outside the exponential function. A numerical solution approach is recommended, with suggestions to use the Lambert W function or Newton's method for faster convergence. The conversation emphasizes the iterative nature of solving such equations, particularly when dealing with air drag effects represented by the constant k.
PREREQUISITES
- Understanding of horizontal projectile motion equations
- Familiarity with exponential functions and their properties
- Knowledge of numerical methods for solving equations
- Basic grasp of the Lambert W function and Newton's method
NEXT STEPS
- Research the Lambert W function and its applications in solving transcendental equations
- Learn about Newton's method for numerical root-finding
- Explore iterative methods for solving equations with exponential terms
- Study the effects of air resistance on projectile motion
USEFUL FOR
Students and professionals in physics, mathematics, and engineering who are tackling complex projectile motion problems, particularly those involving air drag and numerical solutions.
What you are describing (I think!) is one very crude way of solving an equation iteratively.