a. Consider a (spherical) pebble of radius 1 cm falling under the influence of gravity. Assume it experiences a quadratic drag force (i.e., proportional to the velocity squared). Assume the constant of proportionality for the drag force is the product of a constant κQ and a geometric factor is the square of the radius. Assume the density of stone is 2500 kg/m3 and that κQ = 0.87 kg/m3 . Estimate the terminal velocity of the pebble (vT ). b. Consider the microscopic spherical droplet of oil (of radius r) moving under the influence of gravity that R.A. Millikan used to determine the elementary electric charge. The oil droplet fell vertically between two parallel plates. Before turning on the voltage between the two plates (so to create a uniform electric field in between), Millikan measured the terminal velocity of the drop (vT ) and compared to theory to estimate the drop radius. He assumed the drop experiences a linear drag force (i.e., proportional to the velocity). Assume the constant of proportionality for the drag force (FD) is the product of a constant κL and a geometric factor that goes as the radius (i.e., FD = κLr). Further, assume the density of oil is 800 kg/m3 , κL = 3.1 × 10−4 kg/m·s), and the drop radius is one micron. Estimate vT .

5. Suppose that President Trump were to make the claim that “Our unemployment rate is falling from its level of 2 years ago, this is a strong positive sign of our economic health and vitality.” A Bureau of Labor Statistics report is released, confirming President Trump’s statement; however, the BLS report reveals that in addition to a falling unemployment rate, the labor force has declined as well.

A. You are tasked with job of producing a counter argument to President Trump’s claim of economic “health and vitality” and must do so at a level of Economics used in this course. What is your counter argument? Can you produce a numerical example that would cast doubt on President Trump’s claims?

B. You are tasked with the job of further supporting President Trump’s claim of economic “health and vitality” and must do so at a level of Economics used in this course. What is your counter argument to the claim made in part A. above?

A spherical raindrop falling through fog or mist accumulates mass due to condensation at a rate proportional to its cross-sectional area multiplied by the velocity.
a. Calculate the acceleration of the raindrop in terms of its radius and velocity. The raindrop starts from rest and has almost zero size.
b. If a terminal velocity of 10 m/s is reached at a raindrop radius of 1 mm, find the proportionality constant for the increase in the raindrop's mass with velocity.
c. find the relationship between the raindrop radius, r, and the height dropped, y. [Hint: v = dy/dt]
d. How far does the raindrop fall as it grows to a size of 1 mm?

In the summer of 2008, people began falling ill from listeriosis, a bacteria that can contaminate food. Twenty-two people died and many more were sick. The contamination was traced to Maple Leaf Foods, a large Canadian meat products manufacturer. The company took action to recall its products, identify the source of the contamination, and reassure the public. Today it successfully continues in business.

Course concepts that might apply to this business issue:

• Government regulation: what regulation affected this situation? What was Maple Leaf required to do?

• Operations: were there quality issues, or other operational issues, that played a role in this situation? • Business ethics, social responsibility: what did Maple Leaf do to act as a responsible corporate citizen in this crisis?

• Public relations and crisis management: What did the company do that helped it recover the public’s trust? What could it have done differently, or better?

A small meteorite (30 kg) is falling through the earth’s atmosphere. It is moving very fast - in fact, faster than the terminal velocity it would have reached if had been dropped from a great height. In a situation like this, the drag force is stronger than the weight. At one moment, the magnitude of the meteorite’s acceleration is 4.0 m/s². You need to calculate the magnitude of the drag force on the meteorite.

1. Draw a free-body diagram, which includes an arrow for each individual force on      the meteorite (and labels to indicate the type of force), an arrow for the net force,      and a coordinate system.     

2. In this situation, the velocity of the meteorite and the acceleration of the meteorite point in [the same direction, in opposite directions].

3. In this situation, the velocity of the meteorite and the net force on the meteorite      point in [the same direction, in opposite directions].

4. In this situation, the magnitude of the drag force on the meteorite is [increasing,      decreasing, remailing constant].

5. Write an algebraic expression that shows how the individual forces combine to      produce the net force on the meteorite. The signs in the expression must be

              consistent with the coordinate system in the free-body diagram. (That is, add in      all the forces in the positive direction and subtract all the forces in the negative      direction.)

6. Set that expression equal to ma and solve the resulting equation for the

              magnitude of the drag force. Type out the equation with all known numbers      inserted in their proper places and then just state the answer.

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A country Spartan is falling behind its growth target. It was estimated that GDP must grow by at least $40 bn to achieve the target growth rate. The country is already running in budget deficit. Should the taxes decrease or government expenditure increase to achieve the target growth. Given MPC = 0.25

The Roomba by iRobot is a self-propelled vacuum cleaner that avoids falling off of stairs, vacuums along walls and furniture, and recharges itself. Prices range from $150 - $399.

If you were to buy this product, at what price point do you feel comfortable buying it online or in a retail store?

Which of the following would not be considered pure contractionary fiscal policy?

A. A cut in taxes matched by an equal cut in spending.

B. A cut in spending used to finance a cut in the money supply.

C. A cut in spending in order to buy back some outstanding government bonds.

D. A tax increase used to buy back some outstanding government bonds.

we consider an investor with $5,000 to invest. Assume the spot price in 12 months is $100. Calculate the amount the investor will make spending the $5,000 to buy shares of stock, spending the $5,000 to buy puts with a strike of $100, or spending the $5,000 to buy calls with a strike of $100? Based on this analysis, Why do investors use options? what is the advantage of using options?