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?

A truck is traveling down a road with a 3-percent grade at a speed of $55 \mathrm{mi} / \mathrm{h}$ when the brakes are applied. Knowing the coefficients of friction between the load and the flatbed trailer shown are $\mathrm{m}_s=0.40$ and $\mathrm{m}_k=0.35$, determine the shortest time in which the rig can be brought to a stop if the load is not to shift.

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.

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?

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 an impact between the ball and the tongue of the $2000-\mathrm{kg}$ trailer if the hitch deflects $2.8 \mathrm{~mm}$ dynamically on impact. The tractor weighs $9807 \mathrm{~N}$. The velocity at impact is $0.3 \mathrm{m/sec}$. (also see the 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.

Two hydrofoils are used on the boat that is traveling at $20 \mathrm{~m} / \mathrm{s}$. If the water is at $15^{\circ} \mathrm{C}$, and if each blade can be considered as a flat plate, $4 \mathrm{~m}$ bng and $0.25 \mathrm{~m}$ wide, find the thickness of the boundary layer at the trailing or back edge of each blade. What is the drag on each blade? Assume the flow is completely turbulent.

Use substitution and partial fractions to find the indefinite integral. ∫ √x / (x-4) dx

Find all second partial derivatives of f. v = r cos (s + 2t)

Distinguishing Between Direct Objects, Adverbs, and Objects of Prepositions. In each of the following sentences, underline the direct objects and circle any adverbs or prepositional phrases. Not every sentence has all three. Megan took her brother to the bowling alley regularly for six months.

Tell whether the ratios form a proportion. 6. 8/50, 4/10

Find the total fee.

$$\scriptstyle\begin{array}{|l|l|l|l|} \hline \text { Professional Service } & \text { Fee Structure } & \text { Project Information } & \text { Total Fee } \\ \hline \text { Image Consultant } & \text { 150 per hour } & \text { Worked 4.25 hours } & \\ \hline \end{array}$$

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?

Let ƒ(x) be the function that gives the cost, in cents, to mail a first-class package that weighs x ounces. In August of 2009, the cost was $1.22 for a package that weighed up to 1 ounce, plus 17 cents for each additional ounce or portion thereof (up to 13 ounces). (Source: United States Postal Service.) Sketch a graph of ƒ(x).

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.

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