1. An electron, initially moving in the +x-direction enters a uniform magnetic field in the +y-direction. What is the direction of the initial magnetic force on the electron?

2.

A small light source radiates light uniformly in all directions at a rate of 10 W. What is the light intensity at a distance of 2 m from the source?

After buying a computer system, Sim Thomas must decide whether to purchase (1) a complete maintenance (or service) policy at a cost of $500, which would cover all maintenance costs; (2) a partial maintenance policy at a cost of $300, which would cover some of the costs of maintenance; or (3) no maintenance policy. The consequences, costs and probabilities are given in the following table:

Using EMV, what do you recommend?

Fatima Hopkins, the CEO of Central Adventures, is having difficulties with all three of her top management level employees. With one manager making questionable decisions, another threatening to leave, and the third likely ‘in the red’, Fatima is hoping there is a simple answer to all her difficulties. She is asking you (her accountant) for some advice on how to proceed.

Central Adventures owns and operates three amusement parks in Michigan: Funland, Waterworld, and Treetops. Central Adventures has a decentralized organizational structure, where each park is run as an investment center. Park managers meet with the CEO at least once annually to review their performance, where each park manager’s performance is measured by their park’s return on investment (ROI). The park manager then receives a bonus equal to 10% of their base salary for every ROI percentage point above the cost of capital.

Fatima’s first difficulty is with the Funland park. Funland is an outdoor theme park, with twelve roller coaster rides and several other attractions. This park has first opened 1965, and most of the rides have been in operation for 20+ years. Attendance at this park has been relatively stable over the past ten years. The park manager of Funland, Janet Lieberman, recently shared with Fatima a proposal to replace one of their older rides with a new roller coaster, a hybrid steel and wood roller coaster with a 90 degree, 200 foot drop and three inversions. The proposal indicated that the ride would cost $8,000,000 with an estimated life of 20 years. In addition, this new style of coaster would require additional maintenance and insurance, costing $125,000 each year. However, it projected that this new attraction would boost attendance, earning the park an additional $1,190,000 per year in revenues. Janet ultimately decided not to invest in this new attraction. Fatima (doing a quick mental calculation) saw that the investment had a payback period of eight years—much shorter than the life of the roller coaster—and is perplexed at Janet’s decision.

The second dilemma concerns the Waterworld park. Waterworld is an indoor water park, operating year-round. Run by park manager David Copperfield, Waterworld was built in 2016 and has increased attendance by 20% every year since. David recently sent you an email complaining that, based on the current bonus payout schedule, Janet Lieberman’s bonus last year was significantly higher than his. He points to the increasing attendance, and says that his park is being punished for having opened so recently (his park assets are much more recent than the roller coasters at Funland). He currently has an employment offer from another company at the same base pay rate, which he says he will accept if his performance is not appropriately acknowledged. Fatima needs to look at the relative performance across parks to determine how to proceed with David.

Central Treetops includes a high ropes course and has a series of ziplines that criss-cross over the Chippewa River. For many years, it was a popular venue for corporate team-building activities, so it is equipped with a main indoor facility with cafeteria and overnight guest rooms. This park has lost popularity in recent years, and has been ‘in the red’ for the past two years. If the park is not profitable this year, you will need to decide whether to close it - permanently. Included in the ‘Fixed COGS’ for Treetops is a $86,000 mortgage payment on the land and buildings for the park, which would still need to be paid by Central Adventures if the park is closed. Incidentally, you recently had a conversation with the regional head of the YMCA, who would like to open a summer camp in the central Michigan region. If you decided to close Treetops, you are fairly certain that you could lease that land to the YMCA for $250,000 annually.

A partial report of this year’s financial results for Central Adventures shows the following:

The ‘Selling and administrative costs’ are all incurred directly by each park, and are determined at the beginning of each year (that is, they do not change with the number of tickets sold). In addition to the information above, there are $2,542,920 in corporate costs, which are currently allocated evenly between the three parks. These costs are primarily due to employee benefits costs, which are billed at the corporate level. If the Treetops park is closed, the allocated corporate costs would decrease by $12,000. Central Adventures has a cost of capital of 12 percent (and Fatima uses the cost of capital as their required rate of return) and are subject to 18% income taxes.

Fatima needs to evaluate this year’s performance results before she can make any decisions. Is David’s complaint about the performance evaluation metrics valid? Is that also affecting management decisions in the form of Janet’s rejection of the proposed new rollercoaster? And is the company better off without Treetops? She sets off to the company accountant’s office to help get some answers.

a.     Create a segmented income statement for Central Adventures.

b.     Calculate the current annual ROI, residual income and EVA for the three parks.

c.    why it was/was not in Central Adventure’s overall best interest for Funland to reject the new rollercoaster.

d.     is David Copperfield’s (the Waterworld park manager) complaint valid? Explain why it is (or is not valid), and what further information would be necessary.

e.     why should they close/ not close treetops.

f.      what should you recommend she do to improve the evaluation of park manager performance measurement at Central Adventures.

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 lb and was traveling eastward. Car B weighs 1125 lb and was traveling westward at 47.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 21.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750. How fast (in miles per hour) was car A traveling just before the collision? (This problem uses English units because they would be used in a U.S. legal proceeding.)

A power shovel with a dipper of two cubic yard capacity has a standard operating cycle time of 80 seconds. The excavated material which has a swell factor of 05 will be disposed by a dump truck with an 8 cubic yard capacity at a dump site 6 miles away. The average speed of the dump truck is 30 mph and the dumping time is 40 seconds. Find the daily standard production rates of the power shovel and the dump truck if both are operated 8 hours per day. Determine also the number of trucks needed daily to dispose of the excavated material.

In an experiment to investigate the performance of four different brands of spark plugs intended for use on a 125-cc motorcycle, five plugs of each brand were tested, and the number of miles (at a constant speed) until failure was observed. A partially completed ANOVA table is given.

Fill in the missing entries, and test the relevant hypotheses using a .05 level of significance. (Give the answer to two decimal places.)

TRANSPORTATION ENGINEERING: A multilane highway has four lanes (2 in each direction) and a measured FFS of 55 mph. One upgrade is 5% and 0.62 miles long. Currently trucks are not permitted on the road, but there are 2% busses in the directional volume of 1900 vehicles (PHF is 0.80). Local authorities are considering allowing trucks into the traffic stream. If this is done, they estimate 150 trucks will use this highway during peak hour. Before trucks, the driver population factor is 1, and it goes to 0.97 after trucks. What will be the level of service before and after trucks are allowed on the road.

A gravitational energy storage system uses a railcar system with a train that has a mass of 200,000 kg. The railroad track is 5 miles long and on a 10% grade (10 ft. elevation gain for every 100 ft. horizontal distance)

a. The electric locomotive uses 1.84 GJ of energy to propel the train up the side of the mountain. What is the efficiency of the system as it is “charging”?

b. The electric locomotive produces 1.44 GJ of electrical energy as it is descending the mountain. What is the efficiency of the system as it is “discharging”?

c. What is the “round-trip efficiency” (including charging and discharging) of the railcar system?

Observing the solar system model of concentric circles with center being the sun. The Earth is 1 AU from the sun. 1 AU is equal to about 150 million kilometers (93 million miles). Using a scale factor of 10¹⁰​ meters per astronomical unit (AU); let say that the Earth is 15 meters away from the sun. And let say, Earth takes on an average 365 days to complete a full cycle around the sun.

How far Earth travels in its orbit in one day?   What would be its speed?

​