Air resistance and the best launch angle: a maths EPQ idea
A title to start from
How much does air resistance change the best angle to launch a projectile?
Why it works as an EPQ
The A Level answer, 45°, assumes no air resistance. Adding drag gives a model you solve numerically and compare with data.
Scope and difficulty
Solid. Solid. Linear drag can be solved exactly; quadratic drag needs a numerical method.
The maths
Builds on these A Level topics: Kinematics · Forces and Newton's laws · Differentiation · Numerical methods.
You would learn:
- Differential equations
- Euler's method or a better step method
- Linear and quadratic drag
One possible plan
- Derive the 45° result and state its assumptions.
- Add linear drag, solve the equations and find the best angle.
- Add quadratic drag and solve numerically, checking step size.
- Compare with measurements or published data for a ball and evaluate.
Pitfalls
- Not checking that the numerical answer converges as the step shrinks.
- Choosing drag constants with no justification.
Where to start reading
- Search for: projectile motion quadratic drag optimal angle
- Search for: Euler method step size error
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