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?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Trigonometric model

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?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Trigonometric model

Quizplus · Accepted Answer

The function is a quadratic equation in terms of $x$, which makes it a nonlinear model.

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