Application of kinematics in badminton
In most sports that involve a projectile motion, there is a very simple flight path that the object being projected follows. The object often makes a parabola shape which means that the object rises and falls at the same angle. In badminton however, the projectile motion looks slightly different because it follows the path of a high drag projectile. The shuttlecock that is used in badminton has an open colonial shape which is embedded into a round cork base. Due to the structural build of the birdie which consists of the top being heavier than the feathers, they are extremely aerodynamic stable because regardless of the initial orientation of the birdie, it will always turn to fly cork first. The word drag essentially means that there is a type of resistance, in this case air resistance, that opposes the relative motion of the moving object. The skirt of the shuttlecock is what causes the drag of the motion as the air resists the motion of the birdie. They difference between the high drag projectile and the normal projectile motion is that in badminton, the birdie has an extremely fast initial velocity that slows down rapidly. Due to this, the shuttlecock will never have a perfect projectile motion because the birdie falls at a much steeper angle than the rise, as seen in the picture on the left(Barrow 2013).
The above sequence of images demonstrates the high drag projectile in badminton as the angle that the birdie rises at which when calculated was 50 degrees, is not a steep as the angle that the birdie falls at which when calculated was 70 degrees.
Drag is usually calculated with the equation shown in the picture on the left but since the velocity of the shuttlecock while it is falling is constant, we can assume that the drag force is equal to the force of gravity just in the opposite direction which would be 9.8m/s squared up.
The diagram on the right shows how I calculated the initial resultant velocity to max height. I first found the horizontal displacement using the time and horizontal displacement from the data collection and then found the initial vertical component using trig ratios. Once I found the components, I used Pythagorean therom to solve for initial resultant velocity. This can be seen in the three calculations below.
I then completed the same process but this time I used the vertical displacement and time from when the shuttlecock was at max height until it reached the ground as seen in the picture on the left. These equations can be seen below.
Once I was able to find the initial resultant velocity which is also max speed and the final resultant velocity, for the shuttlecock, I was able to use the big five kinematics equations to solve for acceleration and max height as seen below. I also went back to my video and found the time and displacement for the swing of the racquet so that I was able to solve for velocity and acceleration of the racquet. As seen in the first calculation where I solved for acceleration until max height, the number is negative which means rather than accelerating, the birdie is decelerating as it reaches max height, which is exactly what it is supposed to happen with a high drag projectile.