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The Path of Flight (Trajectory) of a Football Thrown by a Quarterback

question 29

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The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: y(x) =(g2v02cos2θ) x2+(tanθ) x+y0y ( x ) = - \left( \frac { g } { 2 v _ { 0 } ^ { 2 } \cos ^ { 2 } \theta } \right) x ^ { 2 } + ( \tan \theta ) x + y _ { 0 } where y=y = vertical position of football relative to the ground
y0=y _ { 0 } = vertical launch position of football relative to the ground
x=x = horizontal position of football relative to launch position
g=g = magnitude of gravitational acceleration
v0=v _ { 0 } = launch speed
θ=\theta = launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory?

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Definitions:

Participant Observation

A qualitative research method in social sciences where the researcher immerses themselves in the environment of their subjects.

Operationalizing

The process of defining the measurement of a phenomenon that is not directly measurable, by translating it into a form that can be quantified and assessed.

Operational Definitions

Descriptions of concepts in terms of the specific operations or procedures by which they are measured or identified, making them understandable and measurable.

Hypothesis

A proposed explanation for a phenomenon, set forth as a starting point for further investigation.

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