Modelling projectile motion by resolving into independent horizontal and vertical components, using the constant acceleration equations, and finding range, maximum height, time of flight and the equation of the path.

What this dot point is asking

AQA wants you to model projectile motion by treating the horizontal and vertical components separately, apply the constant acceleration equations to each, and find quantities such as range, maximum height, time of flight and the equation of the path. The single big idea is independence of the two components, which turns one hard two-dimensional problem into two straightforward one-dimensional ones.

Resolving the launch

The two components are linked only by the shared time $t$. You set up a suvat treatment for each component using the same $t$, then solve. Time is therefore the bridge between horizontal and vertical motion, and most projectile problems are solved by finding $t$ first.

Key quantities

For maximum height, use $v_y = 0$ at the top with $v_y^2 = (u\sin\theta)^2 - 2gH$. For the impact speed when the projectile lands, combine the horizontal and vertical velocity components with Pythagoras, since speed is the magnitude of the velocity vector.

The equation of the path

Eliminating time between the horizontal equation $x = (u\cos\theta)t$ and the vertical equation $y = (u\sin\theta)t - \frac{1}{2}gt^2$ gives $y$ as a quadratic in $x$, which is a parabola. Substituting $t = \frac{x}{u\cos\theta}$ yields $y = x\tan\theta - \frac{g x^2}{2u^2\cos^2\theta}$. This path equation lets you find the height at a given horizontal distance, or test whether the projectile clears an obstacle.

A general method and the modelling assumptions

Every projectile problem follows the same plan. First, resolve the launch velocity into horizontal and vertical components, $u\cos\theta$ and $u\sin\theta$. Second, set up suvat for the vertical motion (with acceleration $-g$ if up is positive) and note the horizontal motion is at constant velocity. Third, use the shared time $t$ to link the two: find $t$ from one component, then use it in the other. Fourth, answer the question, whether that is a height, a range, a velocity at impact, or a position at a given time.

The model rests on assumptions you should be ready to state and criticise: the projectile is a particle (so its size and spin are ignored), air resistance is negligible (so the only force is gravity and the horizontal velocity stays constant), and $g$ is constant over the flight. Air resistance is the most significant omission: in reality it reduces both the range and the maximum height, and makes the descent steeper than the ascent, so the true path is not a symmetric parabola. Examiners reward candidates who can say how a result would change if air resistance were included.