Describe some optimal control problems in your major field or in another area of interest to you. How difficult would it be to find the optimal controls?

An electron initially located at the origin of a coordinate system is projected horizontally into a uniform electric field with magnitude $E$ and directed upward. If the initial speed of the electron is $v_0$, then its trajectory is

$$x=v_0t\hspace{6pt}y=-\frac{1}{2}\left(\frac{eE}{m}\right)t^2$$

where $e$ is the charge of the electron and $m$ is its mass. Show that the trajectory of the electron is a parabola.

Note:The deflection of electrons by an electric field is used to control the direction of an electron beam in an electron gun.

In the following, name the term defined or answer the question.

A Six Sigma process that is running at the center of its control limits would expect this defect rate.

An airplane circles an airport twice while $5.00 \mathrm{mi}$ from the control tower. Calculate the length of the arc through which the plane travels.

The competitive equilibrium rent in the city of Lowell is currently $1,000 per month. The government decides to enact rent control and establish a price ceiling of$750 per month for apartments. Briefly explain whether rent control is likely to make each of the following people better or worse off.

A landlord who intends to ignore the law and illegally charge the highest rent possible for his apartments

Note that some of the lines of the poem run on as if they’re out of control; they seem too long. Why might the poet have chosen to write this way?

A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 3 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 20 different mechanics (so there were 17 incorrect diagnoses). Let p = P(correct diagnosis), so p is the proportion of all mechanics who would correctly diagnose the problem. What is the mle of p? Is it the same as the mle if a random sample of 20 mechanics results in 3 correct diagnoses?

In a control system, an accelerometer consists of a $4.70-\mathrm{g}$ object sliding on a horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of $0.800 \mathrm{~g}$, the object is to assume a location $0.500 \mathrm{~cm}$ away from its equilibrium position. Find the force constant required for the spring.

In a control system, an accelerometer consists of a 4.70-g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of 0.800 g, the object should be at a location 0.500 cm away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.

After a vehicle receives an oil change and lube job, does the exergy destruction within a control volume enclosing the idling vehicle change? Explain.

When faced with a situation over which you feel you have no sense of control, it is most effective to use ___________ (emotion/problem)-focused coping.

One of the buffer systems used to control the pH of blood involves the equilibrium between $\mathrm{H}_2 \mathrm{PO}_4{ }^{-}$and $\mathrm{HPO}_4{ }^{2-}$. The $\mathrm{p} K_{\mathrm{a}}$ for $\mathrm{H}_2 \mathrm{PO}_4^{-}$is 7.21. (a) Write the Henderson-Hasselbalch equation for this buffer system. (b) What $\mathrm{HPO}_4{ }^{2-}$ to $\mathrm{H}_2 \mathrm{PO}_4{ }^{-}$ratio is needed to maintain the optimum blood pH of 7.40?

A branch manager of a brokerage company is concerned with the number of undesirable trades made by her sales staff. A trade is considered undesirable if there is an error on the trade ticket. Trades with errors are canceled and resubmitted. The cost of correcting errors is billed to the brokerage company. The branch manager wants to know whether the proportion of undesirable trades is in a state of statistical control so she can plan the next step in a quality improvement process. Data were collected for a 30 -day period and stored in Trade.

a. Construct a control chart for these data.

b. Is the process in control? Explain.

c. Based on the results of (a) and (b), what should the manager do next to improve the process?

Look at Table 24.4. What is easier to control—toxic chemicals leaching out of landfills or toxic chemicals in surface runoff? Defend your answer