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, hang the energy bar with ΔEp=mgΔh, 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.
1 Weight: the force of gravity, not the stuff you are made of
Weight is defined as the gravitational force on a mass: W=mg.
Near Earth,
∣g∣≈9.81m⋅s−2
but exam setters accept
9.8
or
10
when estimating.
Parents ' note: Mistaking weight for mass is a mark-killer because the units differ: Newtons vs kilograms.
A projectile launched with speed u at angle θ splits into vxvy=ucosθ,=usinθ.
Horizontal: no net force (ignore drag for now) ⟹vx is constant.
Vertical: constant downward acceleration g.
2.1 Range shortcut
Maximum range on level ground occurs at θ=45∘ when drag is negligible - a popular MCQ.
2.2 Time-of-flight drill
Total airtime t=g2usinθ.
Swap g for 9.8m⋅s−2 only after symbolic work to minimise rounding slips.
3 Work → gravitational potential energy
Work done against a uniform gravitational field lifting a mass by Δh: W=FΔs=(mg)Δh.
Define this as the increase in gravitational potential energy, ΔEp: ΔEp=mgΔh.
3.1 Quick-check questions
Lift (kg)
\( \Delta h \) (m)
\( g \) (\( \pu{m.s-2} \))
\( \Delta E_p \) (J)
\( 5 \)
\( 2.0 \)
\( 9.8 \)
\( \approx 98 \)
Add or tweak rows for self-testing: multiply m, g, Δh and watch the proportionality.
4 Using ΔEp=mgΔh to solve exam problems
Vertical launches: equate gain in Ep to loss in Ek to find maximum height.
Roller-coaster humps: apply conservation of mechanical energy when friction is “negligible”.
Practical Paper 4: convert scale readings (mass) and ruler readings (height) to energy, propagate uncertainties as ± half-square on measured h.
5 When air fights back: drag and terminal velocity
Drag force D grows roughly with v2 for turbulent flow. A falling body accelerates until D=W - that steady speed is terminal velocity.
5.1 Qualitative story line
Early drop: D<W ⇒ downward acceleration ≈ g.
Mid-fall: D↑ with v so net acceleration shrinks.
Terminal phase: net force zero, v constant; energy converts entirely to thermal/air sound, not extra Ek.
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)
Vector split - resolve 15m⋅s−1 at 60∘.
Energy swap - a 0.20kg ball loses 4.9J of Ep; find Δh.
Drag logic - sketch acceleration vs time for a skydiver from exit to parachute deployment.
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=gu2sin2θ) with data-logger labs - the double exposure cements memory.
8 Three WA timing rules (Projectile edition)
Sketch first, solve later - a quick vector diagram prevents sign errors.
Keep symbols until the final line; substitute numbers only once.
One speed check - cross-check horizontal range with vxt 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 vx const; fit a parabola to y(t) to extract g.
Compare measured g to 9.8 and keep the percent error below five percent.
Comprehensive revision pack
9478 Section II, Topic 5 Syllabus outcomes at a glance
Outcome (a) - resolve projectile motion into perpendicular components and describe trajectories.
Outcome (b) - use the kinematics equations in horizontal/vertical directions simultaneously.
Outcome (c) - apply conservation of mechanical energy in projectile contexts.
Outcome (d) - discuss the effects of air resistance qualitatively, including terminal velocity.
Outcome (e) - connect projectile models to real applications (launchers, ballistics, safety calculations).
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
Quantity
Expression
Horizontal displacement
\( x = (u \cos \theta) t \)
Vertical displacement
\( y = (u \sin \theta) t - \tfrac{1}{2} g t^{2} \)
Time of flight (flat ground)
\( t = \dfrac{2 u \sin \theta}{g} \)
Range (flat ground)
\( R = \dfrac{u^{2} \sin 2\theta}{g} \)
Maximum height
\( h = \dfrac{u^{2} \sin^{2} \theta}{2 g} \)
Energy conversion
\( \Delta E_k + \Delta E_p = 0 \) (ignoring drag)
Terminal velocity (rough)
\( v_t = \sqrt{\dfrac{2 m g}{\rho C_{d} A}} \) (A-level context: qualitative use only)
Derivations & reasoning to master
Parabolic equation: eliminate t between x(t) and y(t) to show y=xtanθ−2u2cos2θgx2.
Energy-height check: derive maximum height using Ek to Ep swap and verify equality with suvat method.
Projectile on inclined plane: adjust coordinates and show how range depends on launch angle relative to slope.
Terminal velocity reasoning: equate drag to weight for a skydiver, comment on importance of surface area.
Worked example 1 - projectile clearing a wall
An 18m⋅s−1 kick launched at 38∘ from ground level must clear a wall 22m away and 2.8m high. Does the ball clear it?
Method: compute the time to reach x=22m using x=(ucosθ)t, then substitute into y(t). Compare y with 2.8m and quote the safety margin.
Worked example 2 - projectile landing on slope
A rescue flare is launched at 35∘ relative to the horizontal from a mountain slope that rises at 12∘. Find the distance along the slope where the flare lands (ignore drag).
Strategy: rotate axes or resolve along/normal to the slope; set the height equation equal to the slope relation y=xtan12∘. Solve simultaneously.
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
Which equation gives the highest value of range for a fixed u? - R=gu2sin2θ (maximum at 45°).
What is the vertical velocity at maximum height? - Zero.
How does doubling launch speed affect range (flat ground)? - Range quadruples (proportional to u2).
Why does a heavy skydiver reach higher terminal velocity than a lighter one (same area)? - Greater weight requires larger drag, so speed must increase until drag matches weight.
What energy transfer occurs when a projectile reaches its apex? - Kinetic energy (vertical component) converts to gravitational potential energy.
Revision workflow
Redo past-year projectile problems including different landing heights and slopes.
Practise deriving parabolic trajectory from base equations weekly.
Create a summary sheet of standard projectile results (time, range, height) and paste into formula booklet.
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.
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.
