AQA A-level PE · Paper 2 · Biomechanical movement · Projectile motion

45°?

Speed, angle and height of release decide how far a projectile travels. 45° is only the best angle when release and landing heights are equal (ignoring air resistance). Change one factor at a time and see for yourself.

Horizontal distance0.0m · with air resistance
No air resistance0.0m · the ghost path
Air resistance ÷ weight0.00at release

Flight time 0.00 s · peak height 0.0 m

Shot put
Projectile:
The exam idea, drawn live

Is 45° always best?

Every point on this graph is a full flight at your speed and height. Set the height to 0 m and the ghost peaks at exactly 45°. Raise the release height and the optimum slides below 45°. Drop it below the landing level and the optimum climbs above 45°.

Solid: with air resistance. Dashed: without. The green line is your current angle.

01 · AQA definitions

Learn these word for word

Projectile motion
Movement of a body through the air following a curved flight path under the force of gravity.
Parabola
A uniform curve that is symmetrical about its highest point.
Weight
The gravitational pull that the Earth exerts on a body. Weight = mass × acceleration due to gravity. N
Air resistance
A force that opposes the motion of a body travelling through the air. N
Free body diagram
A clearly labelled sketch showing all of the forces acting on a body at a particular instant in time.
Resultant force
The sum of all the forces acting on a body (the net force).
Parallelogram of forces
A parallelogram showing that the resultant force acting on a projectile in flight is the diagonal of the parallelogram formed by the vectors of weight and air resistance.

Only two forces act in flight: weight and air resistance. Once the object leaves the hand, foot or racket, the performer can no longer apply force to it. "The force of the throw" is never on a free body diagram of a projectile in flight.

02 · Factors

What decides horizontal distance

FactorEffect on horizontal distanceTry it in the lab
Speed of releaseThe greater the speed of release, the greater the horizontal distance travelled. It is the most important factor.Shot put, 40°: go from 10 to 14 m/s
Angle of releaseThe optimum angle depends on release and landing heights:
· equal heights: 45° (ignoring air resistance)
· release height above landing height: less than 45° (e.g. shot put)
· release height below landing height: more than 45° (e.g. basketball shot, golf bunker shot onto a raised green)		Watch the optimum marker on the graph as you change the height
Height of releaseThe greater the height of release, the greater the horizontal distance (same speed and angle), because the projectile spends longer in the air.Shot put: compare 0 m and 2.5 m
Aerodynamic factorsAir resistance shortens the flight. Lift (Bernoulli principle) and spin (Magnus effect) can lengthen or shorten it.Toggle the ghost on the football

Air resistance lowers the real optimum. The lab shows it: a football kicked from the ground peaks at about 42°, and a shuttle's best angle is much lower still. In the exam, still give the AQA answer: 45° for equal heights, less than 45° when release is above landing, more than 45° when release is below landing.

Stretch point. Elite shot putters actually release at about 37–40°, not the 42° the graph gives. The body can produce more force, and so more speed of release, at lower angles. Because speed matters most, a small loss in angle is worth it.

03 · Flight paths

Parabolic or non-parabolic?

The shape of a flight path depends on which force is dominant: weight or air resistance. The air resistance ÷ weight readout tells you straight away.

ProjectileWeightAir resistanceDominant forceFlight path
Shot putLargeVery smallWeightParabolic: symmetrical about its highest point
Football (long kick)ModerateModerateBoth matterSlightly non-parabolic: falls more steeply and lands shorter than the ghost
Badminton shuttleVery smallVery large at the startAir resistanceNon-parabolic: asymmetrical, drops almost vertically at the end

Factors affecting the size of air resistance:

  • Velocity: the greater the velocity, the greater the air resistance
  • Frontal cross-sectional area: the larger the area, the greater the air resistance
  • Streamlining and shape: a streamlined, aerofoil shape reduces air resistance
  • Surface characteristics: a smooth surface reduces air resistance (the shuttle's feathered skirt increases it)

A shuttle has a tiny mass, a large frontal cross-sectional area and a very high initial velocity, so air resistance is many times larger than its weight. It decelerates rapidly, then falls almost vertically near its terminal velocity (about 6–7 m/s).

04 · Diagrams

Free body diagrams and the parallelogram

Rules for the marks:

  • Draw every arrow from the centre of mass of the projectile.
  • Weight always acts vertically downwards.
  • Air resistance acts in the opposite direction to the motion. At the highest point, motion is horizontal, so air resistance is horizontal.
  • Arrow length shows size. Make the relative sizes clear, and label each arrow.

Drawing a parallelogram of forces:

  1. Draw weight and air resistance as two arrows from the same point.
  2. Complete the parallelogram with two dashed lines, each parallel to one of the forces.
  3. The diagonal from the starting point is the resultant force.
Moment to pause the labWhat the resultant shows
Shot put, any pointResultant is almost exactly weight: vertically downwards. Weight is dominant, so the path is parabolic.
Shuttle, just after the strikeResultant points backwards along the line of flight. Air resistance is dominant, so the shuttle decelerates rapidly.
Shuttle, end of flightAir resistance is about equal to weight and opposite to it, so the resultant is close to zero. The shuttle falls at a near-constant (terminal) velocity.
05 · Exam practice

Try, then check

Question 1 · Identify3 marks

Identify three factors that affect the horizontal distance travelled by a projectile.

Show mark scheme
  • Speed of release
  • Angle of release
  • Height of release
  • Aerodynamic factors (accept air resistance / Bernoulli / Magnus effect / spin)

Any three.

Question 2 · Explain3 marks

Explain why the optimum angle of release for a shot putter is less than 45°.

Show mark scheme
  • The shot is released from a height (about 2 m) above the landing height
  • When release height is greater than landing height, the optimum angle is less than 45° (ignoring air resistance)
  • The shot is already in the air for longer because of its release height, so a lower angle gives a greater horizontal component of velocity and a greater distance

Any three. Also accept (extra point): a performer can generate a greater speed of release at a lower angle.

Question 3 · Draw3 marks

Draw a free body diagram to show the forces acting on a shot put at the highest point of its flight.

Show mark scheme
  • Both arrows drawn from the centre of mass of the shot
  • Weight: vertically downwards, labelled, and much longer than air resistance
  • Air resistance: horizontal, opposite to the direction of motion, labelled and very small

Check it: pick the shot put, scrub to the top of the flight and look at the arrows.

Question 4 · Apply3 marks

Using a parallelogram of forces, explain the resultant force acting on a badminton shuttle immediately after it has been struck.

Show mark scheme
  • Weight and air resistance drawn from the centre of mass, with air resistance much larger than weight and opposite to the direction of motion
  • Parallelogram completed; the diagonal shows the resultant force
  • The resultant acts mostly backwards against the motion, so the shuttle decelerates rapidly
Question 5 · Explain6 marks

Explain why the flight path of a shot put is parabolic, while the flight path of a badminton shuttle is non-parabolic.

Show mark scheme
  • Only weight and air resistance act on a projectile in flight
  • The shot has a large mass, so weight is large
  • The shot has a small frontal cross-sectional area, a smooth surface and a relatively low velocity, so air resistance is very small
  • Weight is the dominant force, so the shot follows a parabolic path, symmetrical about its highest point
  • The shuttle has a very small mass, so weight is very small
  • The shuttle has a high initial velocity, a large frontal cross-sectional area and a feathered (rough) surface, so air resistance is very large
  • Air resistance is the dominant force, so the shuttle decelerates rapidly and follows a non-parabolic, asymmetrical path, falling steeply at the end
  • Parallelogram of forces: the resultant on the shot is almost vertical; the resultant on the shuttle acts mainly against its motion

Any six.

Question 6 · Using a sporting example, explain2 marks

Using an example from sport, explain when the optimum angle of release is greater than 45°.

Show mark scheme
  • When the release height is below the landing height (ignoring air resistance), e.g. a basketball shot to a raised hoop or a golf bunker shot onto a higher green
  • A higher angle gives the projectile enough height and time in flight to rise above the target before dropping onto it