Exam 20: Engineering Economics

Many engineering problems are modeled using differential equations with a set of corresponding boundary and/or initial conditions.

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?

The drag force acting on a car can be modeled using the following function: $F_{d}=\frac{1}{2} C_{d} \rho V^{2} A$ where $F _ { d } =$ drag force $C _ { d } =$ drag coefficient $\rho =$ air density $V =$ speed of car relative to air $A =$ frontal area of car The power P required to overcome air resistance can be modeled according to $P = F _ { d } V .$ When analyzing power as a function of velocity P(V), what order is the resulting function?

The gravitational force between two masses is modeled using the following function: $F _ { g } ( r ) = G \frac { m _ { 1 } m _ { 2 } } { r ^ { 2 } }$ where $F _ { g } =$ gravitational force (Newtons) G=6.673\times1 = mass number 1 (kilograms) $m _ { 2 } = \text { mass number } 2 \text { (kilograms) }$ $r =$ distance between centers of masses (meters) Which type of mathematical model is used here to describe the gravitational force?

Calculus is commonly divided into two broad areas:

The rate of change refers to how a dependent variable changes with respect to an independent variable.

What is the name of the following Greek alphabetic character? $\mu$

The simplest form of equations commonly used to describe a wide range of engineering situations is

For many engineering situations, exponential and logarithmic models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

In general, engineering problems are mathematical models of physical situations.

For many engineering situations, nonlinear models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

Hooke's Law describes the relationship between force F and elastic deflection x in a spring according to the following equation: $F = k x$ . Which type of mathematical model is used in Hooke's Law?

The loudness $\beta$ of sound is dependent upon the sound intensity I according to the following equation: $\beta = 10 \log \left( I \times 10 ^ { 12 } \right)$ . Which type of mathematical model is used in this relationship?

The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: $y ( x ) = - 0.002 x ^ { 2 } + 0.7 x + 7$ where $y =$ vertical position of football relative to the ground (ft) $x =$ horizontal position of football relative to launch position ( $\mathrm { ft } )$ How high above the ground is the football when it is 30 yards downfield from the quarterback?

The velocity of an object under constant acceleration can be modeled using the following function: $\quad v ( t ) = v _ { 0 } + a t$ where $v =$ velocity $v _ { 0 } =$ initial velocity $a =$ acceleration $t =$ time Which type of mathematical model is used to describe velocity in this application?

What kind of mathematical model contains derivatives of functions?

The term rate of change always refers to the physical quantity of time.

The position of an object subjected to constant acceleration can be described by the following function: $x ( t ) = x _ { 0 } + v _ { 0 } t + \frac { 1 } { 2 } a t ^ { 2 }$ where x= position () = initial position () = initial velocity (/) a= acceleration /2 t= time () Which type of mathematical model is used here to describe the object's position?

Greek alphabetic characters quite commonly are used to express angles, dimensions, and physical variables in drawings and in mathematical equations and expressions. It is therefore very important to be familiar with these characters in order to communicate with other engineers.