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

Question

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

Quizplus · Accepted Answer

The equation given is a quadratic equation in terms of $x$, which is a characteristic of a nonlinear model. Linear models are first-degree equations, and exponential models involve variables in the exponent, which is not the case here.

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