Common Mistakes in A/L Projectile Questions (and How to Avoid Them)

Projectile motion appears in A/L Combined Mathematics almost every year. The method is short, but small mistakes cost a lot of marks. Here are the most common ones.

Mistake 1: Mixing horizontal and vertical motion

Always treat the two directions separately. For a particle projected with speed $u$ at angle $\alpha$ above the horizontal (ignoring air resistance):

• Horizontal: no acceleration, so $x = (u\cos\alpha)\,t$
• Vertical: acceleration $-g$, so $y = (u\sin\alpha)\,t - \tfrac{1}{2}gt^2$

The only thing linking them is time, $t$.

Mistake 2: Getting the signs wrong

Choose a positive direction (usually upwards) and stick to it. If the particle lands below its starting point, its final $y$ is negative.

Mistake 3: Memorising formulas you can't derive

You may remember the range on level ground:

$R = \frac{u^2 \sin 2\alpha}{g}$

But this only works when the particle lands at the same height it started. Questions often change that. If you can derive it — set $y = 0$, solve for $t$, substitute into $x$ — you can handle any version.

Mistake 4: Forgetting the equation of the trajectory

Eliminating $t$ gives

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

which is the quickest route for "does it clear the wall?" questions.

Mistake 5: Not drawing a diagram

A clear diagram with axes, the origin and the angle marked prevents most sign and direction errors. Examiners give method marks for clear working.

Practise

Do five past paper projectile questions, timed, then check each step against the marking scheme. If you keep losing marks in the same place, book a Math Power Slot in the MathCLINIC.