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.
Question cue
First question to ask
Usually start with
Trap to avoid
"angle", "range", "wall", "time of flight"
What is independent in each axis?
Resolve u into ux
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Chee Wei Jie·Academic Advisor (Physics)
and
uy
, then use vertical motion to find time
Putting g into the horizontal equation
"maximum height"
Is the vertical speed zero at the top?
SUVAT with vy=0, or an energy-height check
Treating the total launch speed as zero at the top
"different landing height"
Is the landing point level with launch?
Use vertical displacement first, then horizontal range
Using the flat-ground range shortcut blindly
"work done against gravity"
Did height change in a uniform field?
ΔEp=mgΔh
Using path length instead of vertical height change
"air resistance", "terminal velocity"
Is drag still changing with speed?
Compare drag with weight and explain the net force
Saying energy is lost instead of transferred to thermal stores
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.
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
Step
Write down
Why it matters
Common trap
Choose positive direction
Usually up and forward are positive
Fixes the signs of ay, sy, and vy
Mixing downward displacement with upward-positive equations
Resolve launch velocity
ux=ucosθ, uy=usinθ
Find time from the axis with enough data
Often the vertical axis, because g and height are known
Time is the bridge back to horizontal range
Using the flat-ground time formula when the landing height is different
Use horizontal motion last
x=uxt when drag is ignored
Horizontal velocity is constant in the ideal model
Adding 21gt2
Worked check: if a ball is launched from ground level at 20m⋅s−1 and 30∘, then uy=10m⋅s−1, so the flat-ground flight time is t=2uy/g≈2.04s. The horizontal speed is ux=20cos30∘≈17.3m⋅s−1, giving a range of about 35.3m.
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) ⟹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)
Δh (m)
g (m⋅s−2)
ΔEp (J)
5
2.0
9.8
≈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.
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 ΔEp=mgΔh for gravitational potential energy changes in a uniform gravitational field (e.g. near the Earth's surface).
(d) recall and use the equation ΔEp=mgΔh to solve problems.
(e) describe qualitatively, with reference to forces and energy, the motion of bodies falling in a uniform gravitational field with air resistance, including the phenomenon of terminal velocity.
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=(ucosθ)t
Vertical displacement
y=(usinθ)t−21gt2
Time of flight (flat ground)
t=g2usinθ
Range (flat ground)
R=gu2sin2θ
Maximum height
h=2gu2sin2θ
Energy conversion
ΔEk+ΔEp=0 (ignoring drag)
Terminal velocity (rough)
vt=ρCdA2mg
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.
Taking g=9.81m⋅s−2:
t=18cos38∘22≈1.55s.
y=(18sin38∘)t−21gt2≈5.39m.
Since 5.39m>2.8m, it clears the wall by about 2.6m.
Worked example 2 - projectile landing on slope
A rescue flare is launched at 30m⋅s−1 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).
Solution (trajectory intersection): with launch point as origin, the projectile path is
y=xtanθ−2u2cos2θgx2.
The slope is y=xtanα with α=12∘. Setting them equal and taking the non-trivial root:
x=g2u2cos2θ(tanθ−tanα)≈60.0m.
Distance along the slope is s=x/cosα, so s≈61.4m.
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.
