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Eclat Institute

A-Level Physics — 5) Projectile Motion & Energy (IP-Friendly Guide)

Download printable cheat-sheet (CC-BY 4.0)

14 Jul 2025, 00:00 Z

TL;DR
Projectile motion = horizontal uniformity + vertical gravity.
Master these two independent components, hang the energy bar with \(\Delta E_p = mg\Delta h\), 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:
\[ \vec{W} = m\vec{g}. \]
Near Earth, \(|\vec{g}| \approx 9.81 \space \pu{m.s-2}\) 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.

2 Two-component thinking: uniform \(v_x\) + constant \(a_y\)

A projectile launched with speed \(u\) at angle \(\theta\) splits into
\[ \begin{aligned} u_x &= u \cos \theta,\\ u_y &= u \sin \theta. \end{aligned} \]
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
\[ t = \frac{2u \sin \theta}{g}. \]
Swap \(g\) for \(9.8 \space \pu{m.s-2}\) only after symbolic work to minimise rounding slips.

3 Work → gravitational potential energy

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

3.1 Quick-check questions

Lift (kg)\(\Delta h\) (m)\(g\) (\(\pu{m.s-2}\))\(\Delta E_p\) (J)
52.09.8\(\approx 98\)

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

4 Using \(\Delta E_p = mg\Delta h\) 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, \(v\) constant; energy converts entirely to thermal/air sound, not extra \(E_k\).

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 \(15 \space \pu{m.s-1}\) at \(\pu{60 ^\circ}\).
  2. Energy swap - a \(0.20 \space \pu{kg}\) ball loses \(4.9 \space \pu{J}\) of \(E_p\); find \(\Delta h\).
  3. 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 \(R = \tfrac{u^2 \sin2 \theta}{g}\)) 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 \(g\) to \(9.8\) with % error (<5%).

10 Further reading

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.

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