Applied mathematics and modelling · Maths EE idea · Ambitious

The best launch angle with air resistance

A research question to start from

How does linear air resistance change the launch angle that maximises the range of a projectile?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A classic result (45°) broken by a realistic assumption, analysed exactly and numerically.

Mathematics you would need

Differential equations
Exponential solutions
Optimisation
Numerical solution of equations

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Solve the equations of motion with linear drag.
Find the range as a function of angle.
Optimise numerically and analyse how the best angle depends on drag.

Scope and difficulty

Ambitious. Ambitious.

Pitfalls

Quadratic drag attempted without the tools.
No limiting checks (drag → 0).

Where to start reading

Search a library catalogue or a university's open lecture notes for: projectile linear air resistance optimal angle Lambert W. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.