Projectile Motion Notes

Projectile Motion

Definition of Projectile Motion

• A projectile is an object propelled into the air or water.
• It is affected only by gravity and air resistance.

Factors Affecting Projectile Motion

1. Air Resistance:
   • Without air resistance, a projectile's horizontal velocity would remain constant.
   • Air resistance significantly affects sports like discus, javelin, and golf, influencing the projectile's aerodynamic characteristics.
2. Gravity:
   • A downward force brings projectiles back to the ground ("what comes up, must come down").
   • It causes objects to accelerate towards the earth at a rate of $9.81m/s^2$. This acceleration is responsible for the parabolic flight path of projectiles.
   • Without gravity, a projectile would keep going forever.

Impact of Gravity and Air Resistance

• Gymnasts in the air are projectiles affected by gravity and air resistance.

Trajectory of a Projectile

• The path of a projectile is its trajectory.
• The trajectory has two components:
  1. Horizontal
  2. Vertical

Horizontal Component

• Affected by air resistance.
• Relates to the horizontal distance covered by a projectile.
• Without air resistance, the horizontal velocity would remain the same.
• Air resistance can either advantage or disadvantage events, such as sprinting; also plays a role in sports, such as shot put.

Vertical Component

• Affected by gravity.
• Relates to the height reached by the projectile.
• Without gravity, a projectile would keep going forever in the same path.

Factors Determining the Flight Path

1. Angle of Release
2. Speed of Release
3. Height of Release

• Coaches and athletes must determine the task's demands to manipulate these variables to achieve their goals.
• Goals include:
  • Maximizing flight time (e.g., NFL punting)
  • Maximizing the vertical component (e.g., Pole Vault)
  • Maximizing the horizontal component (e.g., Golf drive)
• Athletes must create the right combination of speed, angle, and height of release to meet the activity's demands.

Angle of Release

• Determines the trajectory shape.
• Determines the time the object stays in the air and the horizontal distance the object moves, provided all other things are held constant.
• Theoretical optimal angle of release for distance = $45^{\circ}$, provided the height of release and landing height remain equal, and spin and air resistance are not present.

Impact of Different Release Angles

• If all other factors are constant:
  • Angle < $45^{\circ}$:
    • Shorter horizontal distances, shorter vertical distances, and shorter flight times.
    • Useful in sports like throwing in softball, cricket, or a rugby pass.
  • Angle > $45^{\circ}$:
    • Shorter horizontal distances, greater vertical distances, and longer flight times.
    • Useful in sports like High Jump, Pole Vault, and punting in American Football.
• When the landing height and release height are equal, the trajectory of a projectile forms a smooth, symmetrical curve known as a parabola.

Angle of Release Summary

• Angle of release = $45^{\circ}$:
  • Vertical and horizontal velocity are equal
  • Maximum horizontal distance attained
• Angle of release > $45^{\circ}$:
  • Vertical velocity is greater than horizontal
  • Increased height and flight time
  • Decreased horizontal distance
• Angle of release < $45^{\circ}$:
  • Horizontal velocity is greater than vertical
  • Decreased height and flight time
  • Decreased horizontal distance

Height of Release

• The greater the height of release, the greater the horizontal distance covered, provided all other factors are equal.

Optimal Angle Based on Release and Landing Height

• Release height = landing height = $45^{\circ}$ (e.g., kicking a soccer ball from the ground)
• Release height > landing height < $45^{\circ}$ (e.g., Throwing)
• Release height < landing height > $45^{\circ}$ (e.g., Hitting a golf ball onto an elevated green)

Constraints and Sacrifices

• Athletes must not sacrifice release speed for added release height or optimal theoretical angle of release.
• Constraint relationships exist among projection speed, height, and angle.
• When one is shifted closer to what would theoretically be optimal, another moves farther away from being optimal due to human anatomy.
• E.g., During a long jump, the theoretically optimum take-off angle should be $45^{\circ}$. However, taking off at this angle would decrease the horizontal velocity by approximately 50%!

Speed of Release

• The greater the speed or velocity of release, the greater the distance a projectile will carry.
• Release speed is the most critical factor when maximizing distance.
• The projectile's velocity at the instant of release determines the height and length of the trajectory, provided all other factors are held constant.
• The vertical velocity component determines the height of the apex.
• The horizontal component is constant throughout the flight if air resistance = 0 and is determined at the point of release.

Impact of Increasing Release Speed

• Increasing the speed of release has the most significant effect on the distance achieved by the projectile.