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?

When Earth traveled through the storm of meteorites trailing the comet Tempel-Tuttle on November 17, 1998, the storm was 1,000 times as intense as the average meteor storm. Before the comet arrived, telecommunication companies worried about the potential damage that might be inflicted on the approximately 650 satellites in orbit. It was estimated that each satellite had a 1% chance of being hit, causing damage to the satellite’s electronic system. One company had five satellites in orbit at the time. Determine the probability distribution of the number of the company’s satellites that would be damaged.

The tractor-trailer unit is moving down the incline with a speed of 5 mi/hr when the driver brakes the tractor to a stop in a distance of 4 ft. Estimate the percent increase n in the hitch-force component which is parallel to the incline, compared with the force present at steady speed. The cart and its load combined weigh 500 lb. State any assumptions.

The 2-Mg truck is traveling at 15 m/s when the brakes on all its wheels are applied, causing it to skid for a distance of 10 m before coming to rest. Determine the constant horizontal force developed in the coupling C, and the frictional force developed between the tires of the truck and the road during this time. The total mass of the boat and trailer is 1 Mg.

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.

Approximate the sum of each series using the first three terms and find an upper estimate to the error in using this approximation. $\sum_{k=1}^{\infty}(-1)^{k+1} \frac{1}{k^{2}}$

Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M. on a Friday morning. On Sunday morning, you leave the lake at 7 A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car t hours after 7 A.M. on Friday morning and let g(t) be your distance from the car t hours after 7 A.M. on Sunday morning. Evaluate f(0), f(2), g(0), and g(2).

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.

Four hundred people were selected from each of the four geographic regions (Midwest, Northeast, South. West) of the United States, and they were asked which form of camping they prefer. Pop-up camper/trailer, family-style (tenting with restrooms), rustic (tenting, no restrooms), or none were the options. The following table displays the survey's findings.

$$\begin{array}{lcccr} \hline & \text { Midwest } & \text { Northeast } & \text { South } & \text { West } \\ \hline \text { Camper/trailer } & 132 & 129 & 129 & 135 \\ \text { Family style } & 180 & 175 & 168 & 146 \\ \text { Rustic } & 46 & 50 & 59 & 68 \\ \text { None } & 42 & 46 & 44 & 51 \\ \hline \end{array}$$

Can you conclude that the distributions of preferred camping types are different for at least two of the regions based on the evidence from these samples? Use $\alpha=.01$.

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.

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 tractor-trailer truck has a drag area $C_D A=8 \mathrm{~m}^2$ bare and $6.7 \mathrm{~m}^2$ with an aerodynamic deflector (Fig. $7.18 \mathrm{~b}$ ). Its rolling resistance is $50 \mathrm{~N}$ for each mile per hour of speed. Determine the total horsepower required at sea level with and without the deflector if the truck moves at (a) $55\ \mathrm{mi} / \mathrm{h}$ and (b) $75\ \mathrm{mi} / \mathrm{h}$.

A food trailer serves chicken and records the order size and sides on their orders, as shown in the table.

Green Salad: 2 pieces 33 and 3 pieces 13 Macaroni & Cheese: 2 pieces 22 and 3 pieces 55 French Fries: 2 pieces 52 and 3 pieces 65 Cole Slaw: 2 pieces 35 and 3 pieces 55

Explain how to find the experimental probability that the next order is two pieces of chicken with a green salad.

Suppose the wing of an aircraft as a flat plate of $2.5-\mathrm{m}$ length in the flow direction. The plane is moving at $100 \mathrm{~m} / \mathrm{s}$ in air that is at a pressure of $0.7$ bar and a temperature of $-10^{\circ} \mathrm{C}$. The top surface of the wing absorbs solar radiation at a rate of $800 \mathrm{~W} / \mathrm{m}^2$. Assume the wing to be of solid construction and to have a single, uniform temperature. Estimate the steady-state temperature of the wing.