Occasionally, people can survive falling large distances if the surface they land on is soft enough. During a traverse of the Eiger’s infamous Nordvand, mountaineer Carlos Ragone’s rock anchor gave way and he plummeted 500 feet to land in snow. Amazingly, he suffered only a few bruises and a wrenched shoulder. Assuming that his impact left a hole in the snow 4.0 ft deep, estimate his average acceleration as he slowed to a stop (that is, while he was impacting the snow).

A bored boy shoots a soft pellet from an air gun at a piece of cheese with mass $0.25 \mathrm{~kg}$ that sits, keeping cool for dinner guests, on a block of ice. On one particular shot, his $1.2-\mathrm{g}$ pellet gets stuck in the cheese, causing it to slide $25 \mathrm{~cm}$ before coming to a stop. According to the package the gun came in, the muzzle velocity is $65 \mathrm{~m} / \mathrm{s}$. What is the coefficient of friction between the cheese and the ice?

Manufacturers who package their products in cans would like to design the can such that the minimum amount of aluminum is needed. If a soft drink can contains $12 \mathrm{~oz}\ \left(355 \mathrm{~cm}^3\right)$, the function that relates the surface area of the can (the amount of aluminum needed) to the radius of the bottom of the can is given by the equation $f(r)=2 \pi r^2+\frac{710}{r}$, where $r$ is measured in centimeters.

Express the right side of this equation with a common denominator.

Use the following:

$$\begin{array}{l}{\bullet \text { the wave speed equation, } v=f \times \lambda} \\ {\bullet \text { a rearranged form of the speed equation, }} \\ {d=v t} \\ {\bullet \text { the average speed of sound in water or soft }} \\ {\text { tissue, } 1500 \mathrm{m} / \mathrm{s}} \\ {\bullet \text { the speed of light, } 3.0 \times 10^{8} \mathrm{m} / \mathrm{s}}\end{array}$$

Calculate the wavelength of radio waves from an AM radio station broadcasting at 1200 kHz.

Two loudspeakers face each other from opposite walls of a room. Both are playing exactly the same frequency, thus setting up a standing wave with distance $\lambda / 2$ between antinodes. Assume that $\lambda$ is much less than the room width, so there are many antinodes. a. Yvette starts at one speaker and runs toward the other at speed $v_y$. As the does so, she hears a loud-soft-loud modulation of the sound intensity. From your perspective, as you sit at rest in the room, Yvette is running through the nodes and antinodes of the standing wave. Find an expression for the number of sound maxima she hears per second. b. From Yvette's perspective, the two sound waves are Doppler shifted. They're not the same frequency, so they don't create a standing wave. Instead, she hears a loud-soft-loud modulation of the sound intensity because of beats. Find an expression for the beat frequency that Yvette hears. c. Are your answers to parts a and b the same or different? Should they be the same or different?

A "soft x-ray" photon with an energy of $41.8 \mathrm{eV}$ is absorbed by a hydrogen atom in its ground state, knocking the atom's electron out. What is the speed of the electron as it leaves the atom?
A. $1.84 \times 10^5 \mathrm{~m} / \mathrm{s}$
B. $3.08 \times 10^5 \mathrm{~m} / \mathrm{s}$
C. $8.16 \times 10^5 \mathrm{~m} / \mathrm{s}$
D. $3.15 \times 10^6 \mathrm{~m} / \mathrm{s}$
E. $3.83 \times 10^6 \mathrm{~m} / \mathrm{s}$

In each of the following sentences, identify the underlined subordinate clause by writing above it ADJ for adjective clause or ADV for adverb clause.

Example 1. Last summer we visited Niagara Falls, $\overset{\textit{\color{#c34632}{ADJ}}}{{\underline{\text{which is on the border between New York and Ontario}}}}$.

The water continues to erode the soft rock under the falls $\underline{\text{so that the ledges of the falls wear away at a rate of one inch to six feet per year, depending on the volume of water}}$.

A soft-drink machine is regulated so that the amount of drink dispensed averages 240 milliliters with a standard deviation of 15 milliliters. Periodically, the machine is checked by taking a sample of 40 drinks and computing the average content. If the mean of the 40 drinks is a value within the interval $\mu_{\hat{X}} \pm 2 \sigma_{\hat{X}}$ , the machine is thought to be operating satisfactorily; otherwise, adjustments are made. In Section 8.3, the company official found the mean of 40 drinks to be $\overline{x}$ = 236 milliliters and concluded that the machine needed no adjustment. Was this a reasonable decision?

The following statements (numbered here for convenience) are excepted from a description of the element lead in a reference handbook: i. The molecular mass of lead is 207.2. ii. Its elemental symbol is Pb. iii. It is a bluish-white metal of bright luster. iv. Lead has a density of $11.3 \mathrm{g} \cdot \mathrm{cm}^{-3}$. v. It is very soft, highly malleable, ductile, and a poor conductor of electricity. vi. Lead has a melting point of $327.462^{\circ} \mathrm{C}$ and a boiling point of $1749^{\circ} \mathrm{C}$.

The exercise involves mixtures. For thousands of years, gold has been considered one of Earth's most precious metals. One hundred percent pure gold is $24$-karat gold, which is too soft to be made into jewelry. In the United States, most gold jewelry is $14$-karat gold, approximately $58 \%$ gold. If $18$ -karat gold is $75 \%$ gold and 12-karat gold is $50 \%$ gold, how much of each should be used to make a $14$-karat gold bracelet weighing $300$ grams?

The beat frequency is the frequency of the loud and soft sounds heard when two sounds create beats. It is calculated by subtracting the frequencies of the two different sound waves. For example, playing 322-Hz and 324-Hz sounds will result in a beat frequency of 2 Hz. Suppose you strike two tuning forks and hear a beat frequency of 4 Hz. One tuning fork has a frequency of 440 Hz. Can you determine the frequency of the other fork? Explain.

What a big tax on soft drinks can do A big tax on sugary drinks in Mexico has cut consumption. Sellers passed on the entire tax in higher prices. The largest consumers of sugary drinks are the poor who suffer from diabetes and obesity

What can we say about the incidence of Mexico’s tax on sugary drinks and what can we infer about the elasticities of supply and demand for these drinks? Would this tax be a progressive tax or a regressive tax? On the basis of what principle would this tax be fair?

A soft drink company recently surveyed 12,467 of its customers and found that approximately 14 percent of those surveyed purchase one or more energy drinks per week. Of those customers who purchase energy drinks, approximately 64 percent of them prefer citrusflavored energy drinks. Write a program that displays the following:

• The approximate number of customers in the survey who purchase one or more energy drinks per week
• The approximate number of customers in the survey who prefer citrus-flavored energy drinks

A soft drink company recently surveyed 12,467 of its customers and found that approximately 14 percent of those surveyed purchase one or more energy drinks per week. Of those customers who purchase energy drinks, approximately 64 percent of them prefer citrus flavored energy drinks. Write a program that displays the following:

• The approximate number of customers in the survey who purchase one or more energy drinks per week.
• The approximate number of customers in the survey who prefer citrus flavored energy drinks.