A plane traveling horizontally at 80 m/s} over flat ground at an elevation of 3000 m releases an emergency packet. The trajectory of the packet is given by

$$x=80 t, \quad y=-4.9 t^2+3000, \quad \text { for } t \geq 0,$$

where the origin is the point on the ground directly beneath the plane at the moment of the release. Graph the trajectory of the packet and find the coordinates of the point where the packet lands.

A recently graduated mechanical engineer wants to build a reserve fund as a safety net to pay his expenses in the unlikely event that an unexpected emergency arises. His aim is to have $45,000 developed over the next 3 years, with the proviso that the amount must have the same purchasing power as$45,000 today. If the expected market rate on investments is 8% per year and inflation is averaging 2% per year, find the annual amount necessary to meet his goal.

The temperature T (in degrees Fahrenheit) of a patient t hours after arriving at the emergency room of a hospital at 10:00 P.M. is given by $T(t)=98.6+4 \cos \frac{\pi t}{36}, \quad 0 \leq t \leq 18$. Find the patient’s temperature at (a) 10:00 P.M., (b) 4:00 A.M., and (c) 10:00 A.M. (d) At what time do you expect the patient’s temperature to return to normal? Explain your reasoning.

Study of why EMS workers leave the job. A study of fulltime emergency medical service (EMS) workers published in the Journal of Allied Health (Fall 2011) found that only about $3 \%$ leave their job in order to retire. (See Exercise $3.45$, p. 158.) Assume that the true proportion of all fulltime EMS workers who leave their job in order to retire is $p=.03$. In a random sample of 1,000 full-time EMS workers, let $\hat{p}$ represent the proportion who leave their job in order to retire. Describe the properties of the sampling distribution of $\hat{p}$.

Police cars, ambulances, and other emergency vehicles are required to carry road flares. One of the most important features of flares is their burning times. To help decide which of four brands on the market to use, a police laboratory technician measured the burning time for a random sample of 10 flares of each brand. The results were recorded to the nearest minute. Repeat Part b using Tukey’s method.

O A door in a hospital has a pneumatic closer that pulls the door shut such that the doorknob moves with constant speed over most of its pach. In this part of its motion, (a) does the doorknob experience a centripetal acceleration? (b) Does it experience a tangential acceleration? Hurrying to an emergency, a nurse gives a sharp push to the closed door. The door swings open against the pneumatic device, slowing down and then reversing its motion. At the moment the door is open the widest, (c) does the doorknob have a centripetal acceleration? (d) Does it have a tangential acceleration?

In an emergency, it is sometimes the practice of medical professionals to immerse a patient who suffers from heat stroke in an ice bath, a mixture of ice and water in equilibrium at $0 ^ { \circ } \mathrm { C }$, in order to reduce body temperature is $40.8 ^ { \circ } \mathrm { C }$ must have her temperature reduced to the normal range, how much heat must be removed? (b) If she is placed in a bath containing 7.5 kg of ice, will there be ice remaining in the bath when her body temperature is $37.0 ^ { \circ } \mathrm { C } ?$ If so, how much? If not, what will the final water temperature be?

Walking to her car after her 65th birthday party, Mrs. Schultz tripped on ice and fell forward on her outstretched palms. When she arrived at the emergency room, her right wrist and hand were bent like a fork. Dr. Jefferson felt that the styloid process of her radius was outside of the anatomical snuff box and slightly proximal to the styloid process of the ulna. When he checked her elbow, he found that the olecranon lay 2 cm proximal to the two epicondyles of the right humerus. Explain all these observations, and describe what had happened to Mrs.Schultz’s limb.

You are working in the emergency department (ED) of a community hospital when the ambulance arrives with A.N., an $18$-year-old woman who was caught in a house fire. She was sleeping when the fire started and managed to make her way out of the house through thick smoke. The emergency medical system crew initiated humidified oxygen at $15 \mathrm{~L} / \mathrm{min}$ per nonrebreather mask and started a $16$-gauge IV with lactated Ringer's solution. On arrival to the ED, her vital signs are $100/66, 125, 34$, $\mathrm{SaO}_2 93 \%$. An additional $16$-gauge IV is inserted. She appears anxious and in pain.

Eighteen hours after the injury, the NAP reports these vital signs for A.N. and states that the urine output for the past hour was $20$ mL.

$$\begin{aligned} &\text { Vital Signs }\\ &\begin{array}{ll} \text { Blood pressure } & 90 / 50 \mathrm{~mm} \mathrm{Hg} \\ \text { Heart rate } & 110 \text { beats } / \mathrm{min} \\ \text { Respiratory rate } & 24 \text { breaths } / \mathrm{min} \end{array} \end{aligned}$$

What do you suspect is occurring, and why does this concern you?

A group of hikers is lost in a national park. Two ranger stations have received an emergency SOS signal from the hikers. Station B is 75 miles due east of station A. The bearing from station A to the signal is S 60° E and the bearing from station B to the signal is S 75° W. A rescue party is in the park 20 miles from station A at a bearing of S 80° E. Find the distance and the bearing the rescue party must travel to reach the lost hikers.

(Use Excel) Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is operating normally, "yellow" indicates it is down waiting on personnel for set up or repair, "blue" indicates it is down waiting on materials to be delivered, and "red" indicates an emergency condition. Management has set realistic goals whereby the assembly line should be operating normally 80% of the time, waiting on personnel 9% of the time, waiting on materials $9 \%$ of the time, and in an emergency condition 2% of the time. Based on $250$ recent status records, the status was green $185$ times, yellow $24$ times, blue $32$ times, and red $9$ times.

a. State the appropriate null and alternative hypotheses to test if the proportions of assembly line statuses differ from the goals set by management.

b. Calculate the value of the test statistic.

c. Use Excel's CHISQ.DIST.RT function to calculate the $p$-value.

d. Are management's goals being met at $\alpha=0.05$ ? Will your conclusion change at $\alpha=0.01$ ?

Which of the following most directly changed the legal status of African Americans established by the Supreme Court's Dred Scott v Sandford decision? a. Emancipation Proclamation (1862) b. Thirteenth Amendment (1865) c. Fourteenth Amendment (1868) d. Fifteenth Amendment (1870)

A vehicle is stuck on the railroad tracks as a 430,000 lb locomotive is approaching with a speed of 75 mph. As soon as the problem is detected, the locomotive’s emergency brakes are activated, locking the wheels and causing the locomotive to slide. If the coefficient of kinetic friction between the locomotive and the track is 0.45, what is the minimum distance d at which the brakes must be applied to avoid a collision? What would that distance be if instead of a locomotive, there was a $30 \times 106 lb$ train? Treat the locomotive and the train as particles, assume that the railroad tracks are rectilinear and horizontal, and note that only the locomotive’s brakes are applied.

The frequency distribution shows the number of medical tests conducted on 30 randomly selected emergency room patients.

If a patient is selected at random, find these probabilities:

a. The patient had exactly 3 tests done. b. The patient had at most 2 tests done. c. The patient has 1 or 2 tests done. d. The patient had fewer than 3 tests done. e. The patient had at least 3 tests done.