# Chad Trudo.  In class projectile motion problems only focused on one force – gravity (y direction)  Additional forces such as drag changes components.

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 In class projectile motion problems only focused on one force – gravity (y direction)  Additional forces such as drag changes components such as trajectory, spin, lift, etc. significantly affect projectile motion

 Drag: resistance to forward motion experienced by objects moving through a fluid/air  In class, we focused on gravity (y direction) but the drag force acts directly opposite the movement of the object (x, y, or both)

y V F x x F y F  Skydiving – example of drag in the y direction  Projectile Motion - drag occurs in both the x and y direction  Occurs at one point in time  Drag forces constantly change because angle changes

 A softball thrown at 30 mph on a calm day will produce an airflow around the ball in the opposite direction of 30 mph  If the ball were thrown into a 5-mph headwind, the airflow velocity around the ball would be 35 mph The magnitude of the air resistance is directly proportional to the objects velocity

 F d - Drag Force – the direction of force is opposite the direction of oncoming fluid/air flow (x, y, or both)  Equation expressed as a negative number  p – is the density of the fluid/air Density of air is approximately 1.29 kg/m 3

 V – represents the velocity or speed of the object relative to the air Critical component of drag force because velocity is squared As velocity increases, drag force increases significantly Ex. V increases from 20 mph to 40 mph  Equation is 4x bigger  A – is the frontal surface area (FSA) of the object Decreasing the FSA will allow objects to cut through the air easier and faster The approximate FSA of baseball is between about 12.9 and 13.6 in² "Normal" FSA for a sprinter is generally taken to be.865 m² for an adult

 C d - drag coefficient – dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment (depends upon shape, inclination, flow of air) According the NASA, the C d (Drag Coefficient) of a baseball is approximately.3 C d for the average human ranges from 1 – 1.3 C d is correlated with surface area  a lower drag coefficient indicates the object will have less of a drag force  v - is the unit vector indicating the direction of the velocity- x or y depending upon movement

 FSA and C d are two concepts that are sometimes difficult to understand FSA is a frontal area measurement of the object C d focuses more on how the objects cuts through the fluid

 Example of air resistance/drag forces at play during a skydive. http://www.youtube.com/watch?v=ur40O6nQHsw& NR=1 http://www.youtube.com/watch?v=ur40O6nQHsw& NR=1  In the F d equation the only variables changing are the velocity (V) and the drag coefficient (C d )  Terminal Velocity – when speed or velocity is constant due the restraining force exerted by the air (occurs twice during dive)

 Drag is a very critical force that affects us everyday (walking, throwing, driving etc.)  Drag force is and will continue to be researched because of its role in sports performance

 Benson, Tom. (2008, July 11). Drag on a baseball. Retrieved from http://www.grc.nasa.gov/WWW/K-12/airplane/balldrag.html  Benson, Tom. (2009, April 09). The drag coefficient. Retrieved from http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html  Drag Coefficient. (2009). Wikipedia. Retrieved (2009, December 4) from http://en.wikipedia.org/wiki/Drag_coefficient  Elert, Glenn. (2006). Density of air. Retrieved from http://hypertextbook.com/facts/2000/RachelChu.shtml  Hamilton, Nancy, Weimar, Wendi, & Luttgens, Kathryn. (2007). Kinesiology. McGraw-Hill Humanities/Social Sciences/Languages.  Physics of sky diving. (2008). [Web]. Retrieved from http://www.youtube.com/watch?v=ur40O6nQHsw  Terminal Velocity. (2009). Wikipedia. Retrieved (2009, December 4) from http://en.wikipedia.org/wiki/Terminal_velocity

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