IB Sports, exercise and health science B.2.2.1 Projectile Motion and the Effects of Forces on Flight Path Notes

Projectile Motion in Sport

1. This motion is shaped by six key factors:
   1. Initial velocity
   2. Angle of projection
   3. Height of release
   4. Gravity
   5. Air Resistance
   6. Spin

Key Factors Affecting Projectile Motion

1. Initial velocity:
   1. Starting speed of the projectile
   2. Affects both distance and height
   3. Determines overall range
2. Angle of projection:
   1. Launch angle relative to horizontal
   2. Optimal angle depends on goal
   3. Different for each sport
3. Height of release:
   1. Starting height above landing point
   2. Affects flight time and range
   3. Critical in sports like basketball and volleyball

Optimal Angles in Sport

1. Level ground projectiles:
   1. 45° maximises range
   2. Used in shot put
   3. Ideal for horizontal targets
2. Elevated targets:
   1. Above 45° for basketball
   2. 50-60° for volleyball serves
   3. Higher angles increase peak height

Idealised projectile motion uses two independent velocity components

1. In the idealised case with no air resistance, horizontal velocity stays constant because no horizontal force acts.
2. Vertical velocity changes under gravity, slowing on the way up and speeding up on the way down.
3. The resulting path is a symmetric parabola.
4. Flight time depends only on the vertical component of the launch velocity.

Initial velocity determines projectile range and height

1. The range of a projectile is proportional to the square of its initial velocity.
2. Doubling launch speed roughly quadruples the range.
3. A 10% increase in release speed produces roughly a 21% increase in range.
4. Horizontal velocity: Determines how far the projectile travels.
5. Vertical velocity: Determines how high the projectile rises.

Angle of projection determines range and height

1. The angle of projection is the angle between the projectile's path and the ground at launch.
2. This angle affects the projectile's range, height, and trajectory shape.

Key angles to remember

1. 45°: Maximises range when the launch and landing heights are the same.
2. Less than 45°: Optimal when launching from a height (e.g., shot put).
3. Greater than 45°: Optimal when aiming for a higher target (e.g., basketball free throw).
4. When release height equals landing height and air resistance is negligible, the maximum range is achieved at exactly 45°.
5. When release height is greater than landing height, the optimal angle drops to 30° to 40° (shot put, javelin, discus).
6. When release height is less than landing height, the optimal angle climbs to 52° to 55° (basketball free throw).
7. When air resistance is significant, the optimal angle falls because air resistance disproportionately slows down high, slow trajectories.

Height of release affects flight time and range

1. The height of release is the vertical distance between the launch point and the landing point.
2. A higher release height generally increases the projectile's range.

Gravity

1. Constantly pulls the projectile downward, causing it to follow a curved path (parabola).
2. The vertical velocity decreases on the way up, reaches zero at the peak, then increases downward due to gravity.

Air Resistance (Drag)

1. Opposes motion, slowing the projectile down, particularly in high-speed sports (e.g., golf, cycling).
2. More noticeable in objects with large surface areas or lightweight objects (e.g., shuttlecocks in badminton).
3. Impact factors:
   1. Object's mass and size
   2. Surface area
   3. Air density
   4. Speed of motion
4. Light vs. heavy objects:
   1. Shuttlecocks fall quickly
   2. Tennis balls curve more
   3. Golf balls travel farther

Spin (Magnus effect)

1. Occurs when a spinning object interacts with the air, creating a difference in pressure that alters its trajectory.
2. Topspin makes a ball dip down faster (e.g., in tennis).
3. Backspin makes a ball stay in the air longer (e.g., a golf shot).
4. Sidespin curves the ball left or right (e.g., a soccer free kick).
5. A spinning ball drags air around it, producing faster airflow on one side and slower airflow on the other.
6. By Bernoulli's principle, the faster-flow side has lower pressure, so a force pushes the ball from high pressure toward low pressure.
7. The trajectory bends in the direction the front of the ball is spinning.

Identifying systematic and random errors in projectile experiments

1. Plotting individual trial data against the predicted parabola makes systematic errors visible as data consistently above or below the predicted curve.
2. Systematic errors come from sources like wind, mis-aligned tracking, or biased launch height.
3. Random errors scatter symmetrically around the predicted curve and come from inconsistent release technique or measurement noise.
4. Treating the two error types separately is a core skill in the IA.

Phases of Projectile Motion

1. Launch Phase: Object is propelled with a given velocity and angle.
2. Ascent Phase: Vertical velocity decreases due to gravity, air resistance opposes the direction of motion.
3. Apex (Peak): Vertical velocity reaches zero before the object begins descending.
4. Descent Phase: Gravity accelerates the projectile downward, air resistance continues to oppose the direction of motion.
5. Landing: The projectile reaches the ground or target.

Practical Applications in Sports

1. Basketball Free Throws: Players must consider the angle of projection (usually 52° to 55°) to account for the hoop's height and air resistance.
2. Golf Drives: Golfers use backspin to generate lift, counteracting gravity and extending the ball's flight.
3. Long Jump: Athletes optimize their take-off angle (18°–27°) to balance horizontal speed and vertical lift.
4. Team Sports:
   1. Football free kicks (curved paths)
   2. Rugby conversion kicks
   3. Basketball jump shots
5. Track and Field:
   1. Javelin throw (optimizing distance)
   2. Long jump (balancing height/distance)
   3. Shot put (maximizing range)

Environmental Factors

1. Temperature, humidity, air pressure, wind, and altitude all shift the forces on projectiles during flight.
2. These environmental factors are covered in detail at HL.