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What are the factors that affect how far a golf ball will travel while in…
What are the factors that affect how far a golf ball will travel while in headwind?
Launch angle
In the absence of air and wind resistance. The launch angle affects the vertical and horizontal components of the ball, with the vertical component determines the height while the horizontal component determines the distance it travels.
If the launch angle is
=45°
- It will produce the maximum vertical and horizontal component, as distance = sin(2θ)v^2/g, where sin(2 x 45°) = 1, and any other angle will result in a value smaller than 1
If the launch angle is
>45°
- The horizontal component of initial velocity decreases. Meaning the ball will have a more vertical distance and time, but not as much horizontal velocity to cover the horizontal distance, overall reducing the distance travelled
If the launch angle is
<45°
- The vertical component of initial velocity decreases. This means the ball will cover less vertical distance and the reduced time spent in the air can limit the overall distance travelled.
Gravitational force
F = G(m1m2)/R^2 - The gravitational force is the force between 2 objects and mass (the earth and a golf ball) and their distance between centres. And according to Newton's law of universal gravity, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
Increasing gravitational force
- Increasing gravitational force will decrease the distance the golf ball travels. As Force ∝ 1/distance^2
Decreasing gravitational force
- Decreasing gravitational force will decrease the distance the golf ball travels. As Force ∝ 1/distance^2
Rotational energy
The formula E_rotational= 1/2 Iw^2 demonstrates how rotational kinetic energy affects the range of a ball in the air. The golf ball's rotational energy is determined by two factors; How rapidly the golf ball spins in the air and how much mass the golf ball has.
When mass increases
, the rotational speed of the marble increase (M∝I) & (l∝E). The mass of the marble greatly affects the rotational kinetic energy, hence increasing the range of the marble.
When rotations increase
, the angular velocity increases as well (E∝w^2). Hence increasing the distance as distance is directly proportional to rotational kinetic energy
Initial velocity
Initial velocity is directly related to distance. The greater the speed of release, the greater the distance covered in flight. (S∝V0)
Having a
higher initial vertical velocity
will increase the height of the trajectory, resulting in a longer flight path.
Having a
higher initial horizontal velocity
will increase the length of the flight time and therefore the distance covered.
Air resistance (drag)
Air resistance is a constant force opposing an object's motion on Earth. In projectile motion, air resistance acts in the opposite direction to the motion of the ball, gradually slowing it down, causing the ball to reach its terminal velocity quicker. As a result, the projectile takes longer to cover the same horizontal distance compared to the ideal case with no air resistance.
Wind (Speed & Direction)
Wind speed
Wind speed alternately affects the flight of a golf ball by altering the magnitude of the drag force and changing the velocity the ball is travelling. However, the distance is greatly affected by the direction of the wind
Wind direction
Headwind
- The wind creates an additional resistance, increasing the drag force acting on the ball. Resulting in the velocity reduction and overall affecting the distance travelled
Tailwind
- The wind assists the balls motion by reducing the drag force. With less resistance, the ball can maintain its velocity for a longer distance, greatly affecting how far a golf ball travels
Weight
The greater the weight of the golf ball, the greater the influence of gravity upon it. (g∝w). The greater influence of gravity on the golf ball, decreases the vertical component of the ball, which decreases the distanced travelled
Height of release
The total distance is influenced by horizontal and vertical components. When the ball is released at different heights, it will initially possess vertical velocity due to the acceleration by gravity. Due to this, the higher the ball is released, the greater its initial vertical velocity will be. This increased vertical velocity allows the ball to stay in the air for a longer time, covering a greater horizontal distance.
