Projectile motion — AQA A-Level Physics

Projectile motion is a core topic in AQA A-Level Physics that combines kinematics and vector resolution. It describes the motion of an object projected into the air, moving under the influence of gravity alone, assuming negligible air resistance. You will learn to separate motion into horizontal and vertical components, apply suvat equations independently to each axis, and solve problems involving time of flight, maximum height, and range.

This topic is essential for understanding real-world applications such as sports trajectories, projectile weapons, and orbital mechanics. It also builds a foundation for later topics like circular motion and gravitational fields. Mastery of projectile motion demonstrates your ability to handle two-dimensional kinematics and vector decomposition, skills that are frequently tested in exams.

• →Horizontal motion: constant velocity, no acceleration, so horizontal displacement = horizontal velocity × time.
• →Vertical motion: constant acceleration due to gravity (g = 9.81 m s^-2 downwards), described by suvat equations.
• →Independence of horizontal and vertical motions: the two components are independent and linked only by time.
• →Vector resolution: initial velocity must be resolved into horizontal (u cos θ) and vertical (u sin θ) components.
• →Key features: at maximum height, vertical velocity is zero; time to reach maximum height equals time to fall back to same level (for symmetric trajectories).

• State that the only force acting after launch is weight, so the horizontal acceleration is zero and the vertical acceleration is g downwards.
• Resolve the initial velocity into perpendicular components using trigonometry, for example v cos θ horizontally and v sin θ vertically.
• Treat horizontal motion as uniform velocity and vertical motion as uniform acceleration, then link the two directions through the common time of flight.
• Explain that changing the horizontal component does not change the vertical time of flight, because the directions are independent.
• Combine perpendicular velocity components using Pythagoras' theorem to find the magnitude of the resultant velocity at a given instant.
• Select the appropriate equation of uniform acceleration for the direction being considered, using the known and unknown quantities.
• Apply v = u + at, s = ut + ½at², v² = u² + 2as or s = ½(u + v)t correctly to horizontal or vertical motion.
• Use a = 0 horizontally and a = g downwards vertically, taking care with the sign of g.
• Recognise that the time of flight is common to both directions and use it to link horizontal and vertical calculations.
• Solve for quantities such as maximum height, time of flight or horizontal range by substituting values with consistent units.
• States that friction acts in the opposite direction to the relative motion or attempted motion of the projectile through the medium.
• Explains that friction reduces the horizontal component of velocity, so the range is less than for ideal projectile motion.
• Describes that friction causes the trajectory to become asymmetric, with a steeper descent than ascent.
• Identifies that friction depends qualitatively on surface roughness and the normal contact force, and for air resistance increases with speed.
• Applies the qualitative idea to a named situation, such as a ball thrown through air or sliding on a rough surface, without numerical calculation.
• Drag is a fluid resistance force acting in the direction opposite to the body's velocity relative to the fluid.
• Drag magnitude increases with speed, frontal area and fluid density, and depends on the object's shape.
• Lift acts perpendicular to the relative flow direction and is produced when a shape deflects the fluid.
• For a projectile, drag removes energy and reduces both velocity components, lowering range and maximum height.
• Lift can change the vertical motion of a spinning or aerofoil-shaped projectile, so the trajectory is not a simple parabola.
• A valid qualitative explanation links force directions to the resulting change in the velocity vector.
• At terminal speed the drag force equals the weight for a falling object, so the resultant force is zero.
• Zero resultant force means zero acceleration, so the velocity is constant in magnitude and direction.
• Drag increases with speed, so the acceleration of a falling object decreases as it speeds up.
• Terminal speed is a dynamic balance, not a fixed property of the object alone; it depends on shape, mass and fluid.
• Changing the shape, for example by opening a parachute, increases drag and produces a new lower terminal speed.
• States that air resistance is a resistive force acting opposite to the direction of motion through the air.
• Explains that the magnitude of air resistance increases as the speed of the object through the air increases.
• Links increasing drag to changes in resultant force: during ascent, drag adds to weight increasing downward acceleration; during descent, it opposes weight reducing it.
• Applies the idea to projectile motion, noting that drag opposes velocity and so changes both horizontal and vertical motion.
• Recognises that the effect becomes more significant at higher speeds, so the ideal parabolic trajectory is only an approximation.
• Explains that air resistance opposes the velocity of a projectile at every point, reducing both horizontal and vertical velocity components.
• Describes the resulting trajectory as asymmetric, with reduced range, lower maximum height, and a descent that is steeper than the ascent.
• States that a vehicle reaches maximum speed when the driving force equals the total resistive force, giving zero resultant force and zero acceleration.
• Identifies factors affecting maximum speed, such as engine power, air resistance, frontal area, shape, rolling resistance and gradient.
• Explains that increasing speed increases air resistance, so a greater driving force is needed to maintain or increase speed.

• 💡Always draw a diagram and mark the resolved components before substituting values into equations.
• 💡Keep horizontal and vertical quantities in separate columns so that the common time of flight is used correctly.
• 💡Check that each answer has a sensible direction as well as magnitude, especially for velocity at a particular instant.
• 💡Write down the equation you are using before substituting numbers, so the examiner can follow your reasoning.
• 💡Use consistent signs for upward and downward quantities, and state which direction is positive.
• 💡Round only at the end of a calculation and give the unit with every answer.
• 💡Use the phrase 'opposes relative motion' when defining the direction of friction.
• 💡Link friction explicitly to the reduced horizontal range and the asymmetric shape of the trajectory.
• 💡Keep the treatment qualitative: describe effects in words rather than attempting calculations with coefficients.
• 💡Sketch the velocity vector first, then add drag opposite it and lift at 90° to it before writing any explanation.
• 💡Use comparative language such as greater speed gives greater drag, and link each force to the change it causes in the velocity components.
• 💡When asked about projectile motion with drag, state that the path is asymmetric and that range and maximum height are reduced compared with ideal projectile motion.
• 💡Use the sequence weight greater than drag, then weight equals drag, and link each stage to the sign of the acceleration.
• 💡State explicitly that zero resultant force gives zero acceleration and therefore constant velocity.
• 💡When a parachute opens, describe the sudden increase in drag, the upward resultant force and the deceleration to a new lower terminal speed.
• 💡Use the phrase 'opposes motion' or 'acts opposite to velocity' whenever you describe drag.
• 💡When comparing two speeds, state explicitly that the faster object experiences the greater air resistance.
• 💡If a question asks about projectile shape, mention that drag reduces range and makes the path asymmetric rather than a perfect parabola.
• 💡Sketch the ideal and real trajectories side by side to show the asymmetry clearly, ensuring the descent is drawn steeper.
• 💡Use the balance-of-forces argument: at maximum speed, resultant force is zero, so acceleration is zero.
• 💡When listing factors, group them as driving factors and resistive factors to structure your answer.
• 💡Always draw a clear diagram showing the initial velocity vector and its horizontal and vertical components. This helps you avoid resolution errors and gains method marks.
• 💡State your sign convention explicitly (e.g., 'taking upwards as positive') before using suvat equations. This prevents sign errors and shows clear reasoning.
• 💡When asked to find the velocity at a point, remember to combine the horizontal and vertical components using Pythagoras and trigonometry to give magnitude and direction.

• Treating the horizontal velocity as decreasing because of gravity; correct this by stating that gravity acts only vertically, so the horizontal velocity remains constant if air resistance is negligible.
• Assuming a heavier projectile falls faster; correct this by noting that in a uniform field the vertical acceleration is g for all masses when air resistance is negligible.
• Adding horizontal and vertical speeds directly as scalars; correct this by combining perpendicular components with Pythagoras' theorem.
• Using the resultant initial speed instead of the resolved component in a vertical or horizontal equation; correct this by resolving the velocity first.
• Mixing horizontal and vertical quantities in one equation; correct this by keeping the two directions in separate columns.
• Forgetting that at maximum height the vertical velocity is zero while the horizontal velocity is unchanged; correct this by applying v = 0 only to the vertical direction.
• Treating friction as acting in the direction of motion; correct this by stating that friction opposes relative motion or attempted motion.
• Assuming friction only affects vertical motion; correct this by explaining that friction also reduces the horizontal velocity component.
• Believing friction is constant regardless of speed for air resistance; correct this by noting that air resistance increases with speed.
• Treating drag as always vertically upward: correct this by stating that drag is antiparallel to the relative velocity, so it tilts as the projectile moves.
• Confusing lift with the upward normal force from a solid surface: correct this by defining lift as a fluid force perpendicular to the relative flow.
• Assuming drag is constant during flight: correct this by explaining that drag falls as the projectile slows, so the deceleration is not uniform.
• Saying there is no force at terminal speed: correct this by stating that weight and drag are equal and opposite, so the resultant force is zero.
• Claiming the object stops accelerating only because it has reached a maximum possible speed: correct this by explaining that drag has grown until it balances weight.
• Assuming terminal speed is the same for all objects of equal mass: correct this by noting that shape and area affect drag and therefore the terminal speed.
• Treating air resistance as a constant force regardless of speed; correct this by stating that drag grows as speed grows.
• Saying air resistance acts in the direction of motion; correct this by stating it acts opposite to the velocity.
• Assuming air resistance only affects horizontal motion; correct this by noting it opposes the whole velocity vector, so vertical motion is also affected.
• Claiming the projectile still follows a perfect parabola with air resistance; correct this by describing an asymmetric path with reduced range.
• Saying maximum speed occurs when driving force is maximum; correct this by stating it occurs when driving force equals total resistive force.
• Ignoring rolling resistance or gradient and attributing maximum speed only to air resistance; correct this by listing several resistive factors.
• Misconception: At the highest point, the projectile has zero velocity. Correction: Only the vertical component is zero; the horizontal component remains constant.
• Misconception: Acceleration due to gravity depends on the mass of the projectile. Correction: In the absence of air resistance, all objects fall with the same acceleration g, regardless of mass.
• Misconception: The horizontal velocity changes due to gravity. Correction: Gravity acts only vertically, so horizontal velocity remains constant throughout the motion.

1. 1Day 1-2: Review the theory of projectile motion, including independence of horizontal and vertical motion. Watch video tutorials and make concise notes on key equations.
2. 2Day 3-4: Practice resolving initial velocity into components for various launch angles. Solve simple problems for time of flight, maximum height, and range.
3. 3Day 5-6: Attempt more complex problems, such as projectiles launched from a height or at an angle, and those involving velocity at impact. Check your solutions against mark schemes.
4. 4Day 7-8: Complete past paper questions on projectile motion from AQA A-Level Physics. Focus on structuring answers clearly and using correct terminology.
5. 5Day 9-10: Review mistakes and misconceptions. Create flashcards for key formulas and definitions. Test yourself with active recall prompts.

• 📋Calculation questions: Often ask for time of flight, maximum height, range, or velocity at a given point. Advice: Always resolve initial velocity, use suvat separately for each axis, and show all steps.
• 📋Explain questions: May ask why horizontal velocity is constant or why vertical acceleration is independent of mass. Advice: Use precise language, refer to Newton's laws, and avoid vague statements.
• 📋Graph questions: Sketch or interpret graphs of vertical/horizontal displacement, velocity, or acceleration against time. Advice: Remember that horizontal velocity-time graph is a horizontal line, while vertical velocity-time graph is a straight line with negative gradient.
• 📋Practical-based questions: Describe an experiment to investigate projectile motion, e.g., using a ramp and light gates. Advice: Focus on controlling variables, measuring time and distance accurately, and reducing uncertainty.