An airplane wing of 2 m chord length (leading edge to trailing edge distance) and 11 m span flies at 200 km/hr in air at 30$^{\circ}C$. Assume that the resistance of the wing surfaces is like that of a flat plate. a. What is the friction drag on the wing? b. What power is required to overcome this? c. How much of the chord is laminar? d. What will be the change in drag if a turbulent boundary layer is tripped at the leading edge?

A thin plastic panel ( $3 \mathrm{~mm}$ thick) is lowered from a ship to a construction site on the ocean floor. The plastic panel weighs $300 \mathrm{~N}$ in air and is lowered at a rate of $3 \mathrm{~m} / \mathrm{s}$. Considering that the panel remains vertically oriented, compute the tension in the cable.

A tractor-trailer truck is coasting freely, with no brakes, down an $8^{\circ}$ slope at $1000$-$\mathrm{m}$ standard altitude. Rolling resistance is $120 \mathrm{~N}$ for every $\mathrm{m} / \mathrm{s}$ of speed. Its frontal area is $9 \mathrm{~m}^2$, and the weight is $65\ \mathrm{kN}$. Compute the terminal coasting velocity, in $\mathrm{mi} / \mathrm{h}$, for $(a)$ no deflector and (b) a deflector installed.

A food company manufactures five types of 8 oz Trail mix packages using different mixtures of peanuts, almonds, walnuts, raisins, and M&Ms. The mixtures have the following compositions: $$ \begin{matrix} \text{ } & \text{Peanuts (oz)} & \text{Almonds (oz)} & \text{Walnuts (oz)} & \text{Raisins (oz)} & \text{M&Ms(oz)}\\ \text{Mix 1} & \text{3} & \text{1} & \text{1} & \text{2} & \text{1}\\ \text{Mix 2} & \text{1} & \text{2} & \text{1} & \text{3} & \text{1}\\ \text{Mix 3} & \text{1} & \text{1} & \text{0} & \text{3} & \text{3}\\ \text{Mix 4} & \text{2} & \text{0} & \text{3} & \text{1} & \text{2}\\ \text{Mix 5} & \text{1} & \text{2} & \text{3} & \text{0} & \text{2}\\ \end{matrix} $$ How many packages of each mix can be manufactured if 128 lb of peanuts, 118 lb of almonds, 112 lb of walnuts, 112 lb of raisins, and 104 lb of M&Ms are available? Write a system of linear equations and solve.

A model airplane has a wing span of 3.1 ft and a chord (leading edge–trailing edge distance) of 5 in. The model flies in air at 60$^{\circ}F$ and atmospheric pressure. The wing can be regarded as a flat plate so far as drag is concerned. (a) At what speed will a turbulent boundary layer start to develop on the wing? (b) What will be the total drag force on the wing just before turbulence appears?

Doctors Hanson, Dominick, and Borchard are radiologists living in Fargo, North Dakota. They realize that many of the state's small, rural hospitals cannot afford to purchase their own magnetic resonance imaging devices (MRIs). Thus, the doctors are considering whether it would be feasible for them to form a corporation and invest in their own mobile MRI unit. The unit would be transported on a scheduled basis to more than 100 rural hospitals using an 18-wheel tractor-trailer. The cost of a tractor-trailer equipped with MRI equipment is approximately $\$ 1,250,000$. The estimated life of the investment is eight years, after which time its salvage value is expected to be no more than $\$ 100,000$. The doctors anticipate that the investment will generate incremental revenue of $\$ 800,000$ per year. Incremental expenses (which include depreciation, insurance, fuel, maintenance, their salaries, and income taxes) will average $\$ 700,000$ per year. Net incremental cash flows will be reinvested back into the corporation. The only difference between incremental cash flows and incremental income is attributable to depreciation expense. The doctors require a minimum return on their investment of 12 percent.

Compute the payback period of the mobile MRI proposal.

When trailing a car on a highway, you are advised to maintain a trailing distance that is often quoted in terms of car lengths, such as in "stay back by 3 car lengths." Suppose the other car suddenly stops (it hits, say, a large stationary truck). Assume a car length $L$ is $4.50 \mathrm{~m}$, your car speed $v_0$ is $31.3 \mathrm{~m} / \mathrm{s}(70 \mathrm{mi} / \mathrm{h})$, your trailing distance is $n L=10.0 L$, and the acceleration magnitude at which your car can brake is $8.50 \mathrm{~m} / \mathrm{s}^2$. What is your speed just before colliding with the other car if (a) your reaction time $t_r$ to start braking is $0.750 \mathrm{~s}$ and (b) automatic braking is immediately started by your car's radar system that continuously monitors the road? What is the minimum value for $n$ needed to avoid a collision with (c) the reaction time $t_r$ and (d) automatic braking?

Here are three situations in which consumers might need some protection. A motorist asks for a tow rope 'strong enough for my trailer'. It breaks the first time he tries to use it. Do you think the consumer needs some legal protection in these cases? For each example. identify which part of UK consumer protection laws have broken by the business selling the goods.

Chipsealing is a common and relatively inexpensive way to pave a road. A layer of hot tar is sprayed onto the existing road surface and then stone chips are spread over the surface. A heavy roller then embeds the chips in the tar. Once the tar cools, most of the stones are trapped. However, some loose stones are scattered over the surface. They eventually will be swept up by a street cleaner, but if cars drive over the road before then, the rear tires on a leading car can launch stones backward toward a trailing car (Fig, 4.42). Assume that the stones are launched at speed $v_0=11.2 \mathrm{~m} / \mathrm{s}(25$ $\mathrm{mi} / \mathrm{h}$ ), matching the speed of the cars. Also assume that stones can leave the tires of the lead car at road level and at any angle and not be stopped by mud flaps or the underside of the car. In terms of car lengths $L_c=4.50 \mathrm{~m}$, what is the least separation $L$ between the cars such that stones will not hit the trailing car?

From the trailer hitch from the figure has loads applied as shown in the figure. The tongue weight of $980 \mathrm{~N}$ acts downward and the pull force of $4905 \mathrm{~N}$ acts horizontally. Using the dimensions of the ball bracket in the figure, draw a free-body diagram of the ball bracket and find the tensile and shear loads applied to the two bolts that attach the bracket to the channel in the figure, determine the horizontal force that will result on the ball from accelerating a $2000-\mathrm{kg}$ trailer to $60 \mathrm{m/sec}$ in 20 sec. Assume a constant acceleration. (also see the given figures) determine the contact stresses in the ball and the ball cup (not shown). Assume that the ball is $2-\mathrm{in}~ \mathrm{dia}$ and the ill-fitting ball cup that surrounds it has an internal spherical surface $10 \%$ larger in diameter than the ball.

A model airplane has a wing span of $6\ \mathrm{ft}$ and a chord (leading edge-trailing edge distance) of $4.5 \mathrm{in}$. The model flies in air at $60^{\circ} \mathrm{F}$ and atmospheric pressure. The wing can be regarded as a flat plate so far as drag is concerned. (a) At what speed will a turbulent boundary layer start to develop on the wing? (b) What will be the total drag force on the wing just before turbulence appears?

Suppose that you are driving an 18-wheeler tractor-trailer truck along the highway. A car pulls up alongside your truck and then moves ahead very slowly. As it passes, the combined sound of the car and truck engines pulsates louder and softer. The combined sound can be either a sum of the two sinusoids or a product of them.

At what rate is the car's engine rotating?

A random sample of 502 Vail Resorts' guests were asked to rate their satisfaction on various attributes of their visit on a scale of 1-5 with 1= very unsatisfied and 5= very satisfied. The regression model was Y= overall satisfaction score, $X_1$= lift line wait, $X_2$= amount of ski trail grooming, $X_3$= ski patrol visibility, and $X_4$= friendliness of guest services. (a) Calculate the t statistic for each coefficient to test for $\beta_j=0$. (b) Look up the critical value of Student's t in Appendix D for a two-tailed test at $\alpha=.01$. Which coefficients differ significantly from zero? (c) Use Excel to find a p-value for each coefficient.

$$\begin{array}{lcc} \hline \text { Predictor } & \text { Coefficient } & \text { SE } \\ \hline \text { Intercept } & 2.8931 & 0.3680 \\ \text { LiftWait } & 0.1542 & 0.0440 \\ \text { AmountGroomed } & 0.2495 & 0.0529 \\ \text { SkiPatroMisibility } & 0.0539 & 0.0443 \\ \text { FriendlinessHosts } & -0.1196 & 0.0623 \\ \hline \end{array}$$

For elliptic curves, there are nice ways of finding points with rational coordinates (see Ezra Brown’s article “Three Fermat Trails to Elliptic Curves” in the May 2000 College Mathematics Journal). Show that the points (−3, 0) and (0, 3) are on the elliptic curve defined by $y^{2}=x^{3}-6 x+9$. Find the line through these two points and showthat the line intersects the curve in another point with rational (in this case, integer) coordinates.