6.4MechanicsStretch

Projectile Motion Formulae

General formulae for time of flight, maximum height, range and the equation of the path can be derived once, then applied directly. Knowing how they are derived helps you adapt them.

24 min Video by Zeeshan Zamurred Projectiles

Edexcel A Level Maths: 6.4 Projectile Motion FormulaeWatch the full walkthrough before the notes below.

Open on YouTube

What you'll be able to do

Derive the standard projectile formulae
Find the equation of the trajectory
Apply the formulae to problems
Know their assumptions

The trajectory equation

Eliminating $t$ from the component equations gives the path: $y = x tan θ - \frac{g x ^{2}}{2 u ^{2} cos ^{2} θ}$ — a parabola.

y = x tan θ - \frac{g x ^{2}}{2 u ^{2} cos ^{2} θ}

Equation of the trajectory.

1The trajectory equation is quadratic in x.

2So the path is a parabola.

AnswerA parabola.

Tip — The trajectory equation comes from substituting t = x/(u cos θ) into the vertical equation.

Assumptions

These formulae assume no air resistance, constant gravity, and a projectile modelled as a particle. They are idealisations of real motion.

Formula recap

y = x tan θ - \frac{g x ^{2}}{2 u ^{2} cos ^{2} θ}

Trajectory (parabola).

R = \frac{u ^{2} sin 2 θ}{g}

Range (level ground).

Common mistakes to avoid

Forgetting the modelling assumptions.

No air resistance, particle model, constant g.

Misremembering the range formula.

R = u² sin 2θ / g on level ground.

Key takeaways

Trajectory: y = x tan θ − gx²/(2u²cos²θ) — a parabola.
Range on level ground: R = u² sin 2θ / g.
Assumes no air resistance, particle model, constant g.

Test yourself

Ready to lock in Projectile Motion Formulae? Pick a mode and earn XP & Dobloons.