Physical Sciences•6 min read•5 September 2026

Mastering Vertical Projectile Motion in Grade 12

A definitive guide to setting reference directions, choosing the right equation of motion, and avoiding the sign errors that cost the most marks.

Reviewed by , SACE-registered Mathematics & Physical Sciences educator

Vertical projectile motion remains one of the highest-yield topics in NSC Physical Sciences Paper 1. Despite the equations being straightforward, learners consistently lose marks to sign errors in acceleration rather than to the physics itself.

1. Choose your positive direction early

Before writing down any formula, explicitly define which direction is positive. If upward is positive, gravitational acceleration must always be entered as −9,8 m/s2-9{,}8\ \text{m/s}^2.

Key rule to remember

At the maximum height of any vertical projectile, instantaneous velocity is always 0 m/s, even though acceleration remains 9,8 m/s² downward.

2. Step-by-step example

A standard exam question: a ball is thrown vertically upwards from the ground at 15 m/s15\ \text{m/s}. Calculate the maximum height reached.

vf2=vi2+2gΔx⇒Δx=vf2−vi22gv_f^2 = v_i^2 + 2g\Delta x \quad\Rightarrow\quad \Delta x = \dfrac{v_f^2 - v_i^2}{2g}

Substitute vf=0v_f = 0, vi=15 m/sv_i = 15\ \text{m/s}, and g=−9,8 m/s2g = -9{,}8\ \text{m/s}^2 to solve for Δx\Delta x — no time variable needed.

Practice problemGrade 12 Physical Sciences

Which equation of motion requires no time variable?

Show solution
Use vf2=vi2+2gΔxv_f^2 = v_i^2 + 2g\Delta x. Substitute the known values and solve directly for Δx\Delta x without needing a time value at all.

3. Common pitfalls to avoid

  • Mixing signed and unsigned values in the same calculation — once you fix a positive direction, every vector quantity must follow it for the rest of the question.
  • Forgetting that velocity is zero (not acceleration) at the highest point of the flight.
  • Rounding intermediate values instead of carrying full precision through to the final answer.

Want more worked examples like this?

Practise with Grade 12 Physical Sciences past papers