1.

Set-up the appropriate differential equation(s) and solve to derive the general equation of motion for a human sized “dummy” moving vertically (up/down) under the following assumptions:

(a)The initial elevation is h0 ft.

(b)The initial velocity is V0 ft./sec.

(c)All motion vertical (ignore any sideways motion).

(d)The force due to wind is proportional to velocity and in the opposite

direction of velocity.

(e)The “terminal velocity” is 120mph (e.g.   lim t→∞ (V)= 120 mph).

(f)Force = Mass * Acceleration.

(g)Acceleration due to gravity = 32 ft/sec^2

2.

Assume the dummy is ejected from a test balloon and has initial elevation of 10 miles and initial velocity of 100mph (straight up)

(a) Determine and simplify the equation of motion for this situation

(b) Determine the maximum height, hmax, of the dummy

(c)Determine the dummy’s height at time t = 60 sec

(d)Determine when the dummy will hit the ground in seconds

(e)Determine the speed of the dummy at impact

3.

Repeat (2) using Newton’s equations and compare the answers to those obtained from your model

2.) Trade winds are one of the beautiful features of island life in Hawaii. The following data represent total air movement in miles per day over a weather station in Hawaii as determined by a continuous anemometer recorder. The period of observation is January 1 to February 15, 1971.

      26    113   27    72    16    32    17    35    18    21    11    15
      14    50    57    52    33    26    14    20    13    13    19    20
      18    13    28    105   18    11    57    21    18    25    22
      14    22    50    138   16    16    100   34    28    19    19

a.) Find the position of the median.

b.) Determine the median.

c.) Determine the quartiles.

d.) Write out the 5-number summary.

Test for outliers.
e.) Find the inner quartile range by subtracting the third quartile from the first quartile.

h.) Determine the lower and upper limits through the following equations.

ii.) Are there any outliers? If so which data value(s)?

j.) Above an appropriate x-scale, construct a modified boxplot.

3. The regional transit authority for a major metropolitan area wants to determine whether there is any linear relationship between the mileage of a bus and the market resale value of the bus. A very small random sample resulted in the following data:

Bus Mileage Resale Value

(In 1000 of Miles)       (In $1000)

5 58      

3 90

4 85

2 96

5 64

5 57

a. Use the method of OLS to compute the slope and intercept of sample linear regression line. You need to decide which one is the dependent variable. In addition, write down the estimated sample regression line. Show all of your computations.

b. Explain the meaning of estimated sample intercept and slope in the context of this problem and in plain English.

c. Use a level of significance of 0.05 to check if the population slope is statistically equal to or different from zero. What is your conclusion? Why? Make sure the null and alternative hypotheses are explained in plain English. Also, show the decision rule and critical points or the p-value.

d.  Compute the value of coefficient of determination. Explain what it means in the context of this problem and plain English.

The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1 AU (astronomical unit) is the mean distance from Earth to the sun, about 93 million miles.

Astronomers tell us that it is reasonable to model these data with a power function.

(a)

Use power regression to express velocity as a power function of distance from the sun. (Round regression parameters to two decimal places.)

v = 29.73 × d^0.50

v = 21.41 × d^−0.50

v = 29.73 × d^−0.73

v = 29.73 × d^−0.50

v = 21.41 × d^−0.29

(b)

Plot the data along with the regression equation.

(c)

An asteroid orbits at a mean distance of 3 AU from the sun. According to the power model you found in part (a), what is the mean orbital velocity of the asteroid? (Round your answer to two decimal places.)

_______ km/sec

The regional transit authority for a major metropolitan area wants to determine whether there is any linear relationship between the mileage of a bus and the market resale value of the bus. A very small random sample resulted in the following data:

a. Use the method of OLS to compute the slope and intercept of the sample linear regression line. You need to decide which one is the defendant variable. In addition, write down the estimated sample regression line. Show all of your computations.

b. Explain the meaning of estimated sample intercept and slope in the context of this problem and in plain English.

c. Use a level of significance of 0.05 to check if the population slope is statistically equal to or different from zero. What is your conclusion? Why? Make sure the null and alternative hypotheses are explained in plain English. Also, show the decision rule and critical points or the p-value.

d. Compute the value of coefficient of determination. Explain what it means in the context of this problem and in plain English.

The regional transit authority for a major metropolitan area wants to determine whether there is any linear relationship between the mileage of a bus and the market resale value of the bus. A very small random sample resulted in the following data:

a. Use the method of OLS to compute the slope and intercept of the sample linear regression line. You need to decide which one is the defendant variable. In addition, write down the estimated sample regression line. Show all of your computations.

b. Explain the meaning of estimated sample intercept and slope in the context of this problem and in plain English.

c. Use a level of significance of 0.05 to check if the population slope is statistically equal to or different from zero. What is your conclusion? Why? Make sure the null and alternative hypotheses are explained in plain English. Also, show the decision rule and critical points or the p-value.

d. Compute the value of coefficient of determination. Explain what it means in the context of this problem and in plain English.

The manufacturer of a new hybrid sports utility vehicle (SUV) states that it gets an average of 48 miles per gallon (mpg) on the highway. A consumer group suspects that perhaps the new SUV’s gas efficiency is lower than the manufacturer’s statement. Assume that the gas efficiency of the SUV is approximately normally distributed. The consumer group randomly tests 13 of the new SUV’s under similar highway conditions and obtains the following results: 39, 40, 41, 42, 43, 43, 44, 45, 45, 46, 47, 47, 50
1a) Write the hypotheses statements below to test the consumer group’s claim

2) Explain what type of hypothesis testing you will perform and whether conditions are met.

3a) Test this hypothesis using a significance level of α = 5%. Clearly label a sketch with appropriate shading and calculate the test statistic

4 Would you reject or fail to reject the null hypothesis?

5 Using a significance level of α = 5%, write a conclusion in the context of this problem

A friend is looking for an SUV that averages 48 mpg or more on the highway. Would you advise your friend to purchase this new model SUV? Yes or No

Consider a mid-size city of 3,000,000 people in the Cairo city . Suppose that its residents produce, on average, 6.0 kg a day of MSW. At present this waste is being hauled 180 miles away (in a southeasterly direction) where it is being used to fill in an abandoned open pit nickel mine. The mine and deposited wastes abut a shallow marine embayment. Seaweed, shellfish, crustaceans, and fish are harvested from this embayment and eaten by both the local fishermen and their families as well as by the residents of the city.

Facts about the waste:

55 % of the waste is composed of agricultural waste and household non-sewer organics

35 % of the waste is household waste, including paper, glass and plastics

10 % of the waste is a combination of metal, wood, chemical, petroleum, and other miscellaneous materials.

Calculate how much methane could be generated from the anaerobic decay of the landfill waste over a 10 year time period. What, if anything, could be done with this methane? Would more, less, or the same amount of methane be produced if the waste was simply incinerated? Which waste disposal method provides the biggest threat to environmental sustainability and human health? Explain your answer.

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

TaxesˆTaxes^ =  +  Size.

b. Interpret the slope coefficient.

• As Property Taxes increase by 1 dollar, the size of the house increases by 6.91 ft.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.91.

c. Predict the property taxes for a 1,200-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

  TaxesˆTaxes^               

Expanding Universe

For this week’s assignment, please answer EACH of the following questions/prompts,and post them to the drop box as a single document.

1. What is a particle accelerator?
   How do scientists use particle accelerators to study subatomic particles?
2. What particle is exchanged to generate each of the four fundamental forces?
3. What medical technologies (e.g. PET) rely on the physics of elementary particles?
   What are the benefits of noninvasive procedures such as PET?
4. How is astronomy the oldest science?
5. How does the energy produced at the core of the Sun reach the photosphere?
6. Why won’t the Sun become a supernova or black hole?
7. Why does the existence of the cosmic redshift lead to the big bang picture of the universe?
8. If a galaxy is 1,000 Mpc away, how fast is it receding from us?
9. The average temperature of the universe is 2.7 Kelvin. What is that temperature in degrees Fahrenheit?
10. The Milky Way has a radius of approximately 100,000 light years. How many miles is that? How long would it take you to travel across our galaxy if you were traveling at 50% the speed of light (be sure to show your work for full credit)?