After a great deal of experimentation, two Atlantic Institute of Technology senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according to

$$s(t)=-16 t^2+40 t+3,$$

where s is its height (in feet) above the ground t seconds after being released. (a) How high will it go? (b) How long is it in the air?

Solve. Find the cost per mile to the nearest cent.

$$\begin{array}{|c c c c c c c c c c c|} \hline \small\textbf{(Total Daily Cost}& + & \small\textbf{Total Mileage Cost} & +& \small\textbf{Gasoline Cost} & = & \small\textbf{Total Cost)} & \div & \small\textbf{Miles} & = & \small\textbf{Cost per}\\ & & & & & & & &\small\textbf{Driven} & & \small\textbf{Mile}\\ \hline (\$119.95 & + & \$74.40 & + & \$30.53 & = & ?) & \div & 620 & = & ? \\ \hline \end{array}$$

Robert Hofstadter won the 1961 Nobel Prize in Physics for his pioneering work in studying the scattering of 20-GeV electrons from nuclei. (a) What is the $\gamma$ factor for an electron with total energy 20.0 GeV, defined by

$$\gamma=1 / \sqrt{1-u^{2} / c^{2}} ?$$

(b) Find the momentum of the electron. (c) Find the wavelength of the electron. (d) State how the wavelength compares with the diameter of an atomic nucleus, typically on the order of $10^{-14} \mathrm{m}$.

The simplest cost function is the linear cost function, C(x)=mx+b, where the $y$-intercept $b$ represents the fixed costs of operating a business, and the slope $m$ represents the variable costs. Suppose that a small bicycle manufacturer has daily fixed costs of 1800 dollars and each bicycle costs 90 dollars to manufacture. Graph the linear function.

In physics it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft sec from a rooftop 112 feet high is $s=s(t)=-16 t^{2}+96 t+112$ where t is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground. What is the average speed of the ball from t = 0 to t = 2?

Find the total paid.

$$\begin{array}{|c| c c c c c c c c c|} \hline \small\textbf{Company} & \small\textbf{(Number of Shares} & \times & \small\textbf{Cost per Share} & = & \small\textbf{Cost of Stock)} & + & \small\textbf{Commission} & = & \small\textbf{Total Paid}\\ \hline \text{Peaseley} & (1,000 & \times & \small \$40 \frac{1}{2} & = & ?) & + & \$250.00 &=& ?\\ \hline \end{array}$$

Chinese online retailing giant Alibaba recorded over $\$ 240$ billion in sales in $2013$ $-$ more than Amazon and eBay combined. On its busiest day of the year, Alibaba sold $\$ 5.75$ billion of goods, three times more than what all of America spent on all US shopping sites combined in the same $24$ hours. Alibaba is planning to become a public limited company by selling shares on the New York Stock Exchange. This will value the company at $\$ 150$ billion or more. With the capital it raises, Alibaba has plans not only to dominate China, but to launch its own US marketplace.

At first Alibaba's business was a B$2$B marketplace connecting American merchants with Chinese suppliers. It quickly expanded into retail B$2$C operations with Taoboa, where eight million small businesses now list their items. It later up-scaled with Tmall, a shopping site where premium brands such as Apple, Nike and Disney host virtual shops for Chinese consumers. During the last nine months of $2013$ Alibaba made over $\$ 6.5$ billion dollars in revenue from selling fees, nearly half of which was profit. Alibaba's greatest challenge in entering the US market will be to gain customers trust. In the past it's been criticised for allowing dishonest businesses to sell illegal counterfeit goods on its sites. Customers searching for products have to go directly to Alibaba's sites as, unlike most e-commerce companies, it doesn't permit search engines to index its products. Merchants are able list for free on sites like Taobao, but it charges them a premium if they want their goods promoted in its search engine.

One New York customer has used Alibaba on several occasions in recent years. He said that although he wasn't sure whether to trust the site at first, in the end the prices for goods were too competitive to ignore. He was able to buy the products direct from the manufacturers at $10 \%$ of the price he would have paid on a US website.

The arrival of Alibaba will be a worrying prospect for Amazon, which uses its ability to undercut its competition to continue to build its business.

Evaluate the likely impact on American consumers of Alibaba setting up operations in the USA.

Estimate how many 30 lb bags of mulch an average student in your physics class can load into the bed of a pickup truck in 5.0 min. The truck bed is 4.0 ft off the ground. If you assume that the magnitude of the work done on each bag by the student equals the magnitude of the work done on the bag by gravity when the bag is lifted into the truck, what is the average power output of the student? Express your result in watts and in horsepower.

A single firm in a perfectly competitive market is relatively small compared to the rest of the market. What does this mean? How “small” is “small”?

Elite Service Company is a very profitable small business. It has not, however, given much consideration to internal control. For example, in an attempt to keep clerical and office expenses to a minimum, the company has combined the jobs of cashier and bookkeeper. As a result, Steve Evans handles all cash receipts, keeps the accounting records, and prepares the monthly bank reconciliations.

The balance per the bank statement on March 31, 2014, was $5,931.51. Outstanding checks were: No. 206 for$358.53, No. 441 for $292, No. 590 for$283.00, No. 781 for $286.00, No. 782 for$319.47, and No. 783 for $303.14. Included with the statement was a credit memorandum of$175 indicating the collection of a note receivable for Elite Service Company by the bank on March 21. This memorandum has not been recorded by Elite Service.

The company’s ledger showed one cash account with a balance of $6,889.53. The balance included undeposited cash on hand. Because of the lack of internal controls, Steve took for personal use all of the undeposited receipts in excess of$1,591.63. He then prepared the following bank reconciliation in an effort to conceal his theft of cash.

$$\begin{array}{lrr} \text{Cash balance per books, March 31}&&\text{\$\hspace{1pt}6,889.53}\\ \text{Add: Outstanding checks}\\ \qquad\text{No. 781}&\text{\$\hspace{1pt}286.00}\\ \qquad\text{No. 782}&\text{319.47}\\ \qquad\text{No. 783}&\underline{\text{\hspace{5pt}303.14}}&\underline{\text{\hspace{16pt}808.61}}\\ &&\text{7,698.14}\\ \text{Less: Undeposited receipts}&&\underline{\text{\hspace{8pt}1,591.63}}\\ \text{Unadjusted balance per bank, March 31}&&\text{6,106.51}\\ \text{Less: Bank credit memorandum}&&\underline{\text{\hspace{16pt}175.00}}\\ \text{Cash balance per bank statement, March 31}&&\underline{\underline{\text{\$\hspace{1pt}5,931.51 }}}\\ \end{array}$$

Instructions

(c) What principles of internal control were violated in this case?

The windows of your physics laboratory are left open on a night when the temperature outside drops well below freezing. A steel ruler and a wooden ruler were left on the window sill, and when you arrive in the morning they are both very cold. The coefficient of linear expansion of wood is about $5 \times 10^6 \text{~K}^{-1}$. Which ruler should you use to make the most accurate length measurements? Explain your answer.

Add.

$$\small \frac{3}{4} +\small \frac{1}{8}$$

You are working as an appliance salesperson during the summer. One day, your physics professor comes into your store to buy a new refrigerator. Wanting to buy the most efficient refrigerator possible, she asks you about the efficiencies of the available models. She decides to return the next day to buy the most efficient refrigerator. To make the sale, you need to provide her with the following estimates: $(a)$ the highest COP possible for a household refrigerator,

Complete the problem.

$$\begin{array}{|c| c c c c c c c |c|}\hline \small \textbf{Total} &\small \textbf{(Selling Price per Share} & \times & \small\textbf{Number of Shares} & - & \small\textbf{Commission)}& =& \small\textbf{Net Sale} &\small \textbf{Amount of}\\ \small\textbf{Paid} & & & & & & & &\small\textbf{Profit or Loss}\\ \hline \$380 & (\small \$2 \frac{1}{2} & \times & 200) & - & \$26.45 &=& ? & ?\\ \hline \end{array}$$