H2 Physics Projectile Motion Notes | A-Level 9478

Q: What does A-Level Physics: 5) Projectile Motion & Energy Guide cover?
A: From free-fall graphs to terminal velocity tricks, this post decodes Section II Topic 5 of the 2026 H2 Physics syllabus for IP students and parents.

TL;DR
Projectile motion = horizontal uniformity + vertical gravity.
Master these two independent components, use the gravitational potential energy change formula for height changes, then layer in air resistance to see why every skydiver eventually hits a speed cap called terminal velocity. Nail these ideas early and Paper 1 MCQs turn into “spot-the-component” games.

Concrete example: how to use this page

For a ball thrown at an angle, horizontal velocity stays constant while vertical velocity changes under gravity. Solve the vertical motion for time first, then use that time in the horizontal motion.

Find neighbouring mechanics chapters and Paper 2 problem sets via our free H2 Physics notes; it strings this topic together with circular motion, collisions, and electromagnetism refreshers.

Route map: choose the projectile method first

This map prevents the two common overreactions: using range formulae before checking the landing height, or using energy when the question needs time and horizontal distance.

1 Weight: the force of gravity, not the stuff you are made of

Weight is defined as the gravitational force on a mass:
$$\vec{W} = m \vec{g}.$$

Parents' note: Mistaking weight for mass is a mark-killer because the units differ: Newtons vs kilograms.

2 Two-component thinking: uniform $v_x$ + constant $a_y$

A projectile launched with speed $u$ at angle $\theta$ splits into
$$\begin{aligned} v_x &= u \cos \theta, \cr v_y &= u \sin \theta. \end{aligned}$$

Component setup checkpoint

Before substituting into SUVAT, write the two axes as separate mini-problems that share the same time:

launch speed u at angle theta
  -> horizontal: ux = u cos theta, ax = 0, x = ux t
  -> vertical: uy = u sin theta, ay = -g, y = uy t - 1/2 g t^2
  -> same t links the two axes

Worked check: if a ball is launched from ground level at $\pu{20 m.s-1}$ and $\pu{30 ^\circ}$, then $u_y = \pu{10 m.s-1}$

Misconception check: the two components are independent motions, not two separate projectiles. They describe the same projectile at the same time.

Horizontal: no net force (ignore drag for now) $\implies$ $v_x$ is constant.

Vertical: constant downward acceleration $g$.

2.1 Range shortcut

Maximum range on level ground occurs at $\theta = \pu{45 ^\circ}$ when drag is negligible - a popular MCQ.

2.2 Time-of-flight drill

Total airtime
$$t = \frac{2 u \sin \theta}{g}.$$ Swap $g$ for $9.8 \space \pu{m.s-2}$

3 Work → gravitational potential energy

Work done against a uniform gravitational field lifting a mass by $\Delta h$:
$$W = F\Delta s = (mg) \Delta h.$$ Define this as the increase in gravitational potential energy, $\Delta E_p$

3.1 Quick-check questions

Add or tweak rows for self-testing: multiply $m$, $g$, $\Delta h$ and watch the proportionality.

4 Using $\Delta E_p = m g \Delta h$ to solve exam problems

1. Vertical launches: equate gain in $E_p$ to loss in $E_k$ to find maximum height.
2. Roller-coaster humps: apply conservation of mechanical energy when friction is “negligible”.
3. Practical Paper 4: convert scale readings (mass) and ruler readings (height) to energy, propagate uncertainties as $\pm$ half-square on measured $h$

5 When air fights back: drag and terminal velocity

Drag force $D$ grows roughly with $v^2$ for turbulent flow.
A falling body accelerates until $D = W$ - that steady speed is terminal velocity.

5.1 Qualitative story line

1. Early drop: $D < W$ ⇒ downward acceleration ≈ $g$.
2. Mid-fall: $D\uparrow$ with $v$ so net acceleration shrinks.
3. Terminal phase: net force zero, $v$

5.2 IP exam cue

Graphs of $v$ vs $t$ start curved then flatten - mention increasing drag force to earn explanation marks.

6 Mini-drills (5 min each)

1. Vector split - resolve $\pu{15 m.s-1}$ at $\pu{60 ^\circ}$.
2. Energy swap - a $\pu{0.20 kg}$

7 Why IP students should master this early

Integrated-Programme syllabi compact 6 years into 4, so weaker fundamentals snowball fast. Specialised IP tuition classes devote extra drills to vector decomposition and energy bookkeeping, two areas most Year 3 pupils stumble on.

Parent tip: look for centres that pair conceptual tasks (deriving $R = \dfrac{u^{2} \sin 2 \theta}{g}$) with data-logger labs - the double exposure cements memory.

8 Three WA timing rules (Projectile edition)

1. Sketch first, solve later - a quick vector diagram prevents sign errors.
2. Keep symbols until the final line; substitute numbers only once.
3. One speed check - cross-check horizontal range with $v_x t$ before boxing your answer.

9 Bridge to Paper 4 practicals

• Use video-analysis apps to track x-y coordinates of a ball toss.
• Fit a straight line to $x(t)$ to verify $v_x$ const; fit a parabola to $y(t)$ to extract $g$.
• Compare measured

Need structured practice on Projectile Motion and Energy? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.

Comprehensive revision pack

9478 Section II, Topic 5 Syllabus outcomes

Candidates should be able to:

• (a) describe and use the concept of weight as the force experienced by a mass in a gravitational field.
• (b) describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction.
• (c) derive, from the definition of work done by a force, the equation $\Delta E_p = mg\Delta h$ for gravitational potential energy changes in a uniform gravitational field (e.g. near the Earth's surface).
• (d) recall and use the equation $\Delta E_p = mg\Delta h$

Concept map (in words)

Start with a launch speed and angle. Split the velocity into horizontal (constant) and vertical (accelerated) components. Use suvat per axis to find flight time, range and height. Overlay an energy lens (GPE-KE swaps) to double-check heights. Add drag only after the ideal model; terminal velocity emerges when drag balances weight.

Key relations to memorise

Derivations & reasoning to master

1. Parabolic equation: eliminate $t$ between $x(t)$ and $y(t)$ to show $y = x \tan \theta - \dfrac{g}{2 u^{2} \cos^{2} \theta} x^{2}$

Worked example 1 - projectile clearing a wall

An $18 \pu{m.s-1}$ kick launched at $38^\circ$ from ground level must clear a wall $\pu{22 m}$ away and $\pu{2.8 m}$

Method: compute the time to reach $x = \pu{22 m}$ using $x = (u \cos \theta) t$, then substitute into $y(t)$. Compare $y$

Taking $g = \pu{9.81 m.s-2}$:

$$t = \dfrac{22}{18\cos 38^{\circ}} \approx \pu{1.55 s}.$$

$$y = (18\sin 38^{\circ})t - \tfrac{1}{2}gt^{2} \approx \pu{5.39 m}.$$

Since $\pu{5.39 m} > \pu{2.8 m}$, it clears the wall by about $\pu{2.6 m}$.

Worked example 2 - projectile landing on slope

A rescue flare is launched at $\pu{30 m.s-1}$ at $\pu{35 ^\circ}$ relative to the horizontal from a mountain slope that rises at $\pu{12 ^\circ}$

Solution (trajectory intersection): with launch point as origin, the projectile path is

$$y = x\tan\theta - \dfrac{g x^{2}}{2u^{2}\cos^{2}\theta}.$$

The slope is $y = x\tan\alpha$ with $\alpha = 12^{\circ}$. Setting them equal and taking the non-trivial root:

$$x = \dfrac{2u^{2}\cos^{2}\theta\left(\tan\theta-\tan\alpha\right)}{g} \approx \pu{60.0 m}.$$

Distance along the slope is $s = x/\cos\alpha$, so $s \approx \pu{61.4 m}$.

Practical & data tasks

• Use Tracker video analysis to record projectile paths; fit quadratic models and extract $g$.
• Perform a miniature projectile launch with carbon paper to map impact points; compare with theoretical range predictions.
• Investigate drag by dropping coffee filters; plot velocity vs time and identify terminal speed plateau.

Common misconceptions & exam traps

• Forgetting that horizontal velocity remains constant (no horizontal acceleration in ideal model).
• Mixing up sine and cosine when resolving initial velocity.
• Assuming time to rise equals time to fall even when landing height differs from launch height.
• Treating terminal velocity as immediate; emphasise the approach curve.

Quick self-check quiz

1. Which equation gives the highest value of range for a fixed $u$? - $R = \dfrac{u^{2} \sin 2\theta}{g}$ (maximum at 45°).
2. What is the vertical velocity at maximum height? - Zero.

Revision workflow

1. Redo past-year projectile problems including different landing heights and slopes.
2. Practise deriving parabolic trajectory from base equations weekly.
3. Create a summary sheet of standard projectile results (time, range, height) and paste into formula booklet.
4. Sketch qualitative v-t and a-t graphs for motion with and without air resistance.

Practice Quiz

Test yourself on the key concepts from this guide.

10 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Lumen - Projectile Motion
• LibreTexts - Projectile Motion

11 Call-to-action

Parents: Book a 60-min Projectile Motion clinic during the mid-term lull - it pays dividends in every subsequent mechanics topic. Students: Re-create the range-vs-angle graph in your backyard; share the plot with your tutor to earn a bonus quiz pass.

Last updated 14 Jul 2025. Next review when SEAB releases the 2027 draft syllabus.