Nate the Skate was an avid physics student whose main non-physics interest in life was high-speed skateboarding. In particular, Nate would often don a protective suit of Bounce-Tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. In this way, he got a gut feel for the physical properties of collisions and succeeded in combining his two passions.* On one occasion, the Skate, with a mass of 117 kg, including his armor, hurled himself against a 801-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.89 m/s and Nate bounced backward. What were Nate\'s speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground.

2. Every day, you order take-out dinner from the nearby Chinese place and your roommate orders take-out from the shwarma place, which is a little farther away. The Chinese take-out is delivered after an exponential waiting time with mean 10 minutes, whereas the shwarma arrives after an (independent) exponential waiting time with a mean of 20 minutes. Whoever gets their food first always takes pity on the other and shares. (a) Let Sn be the amount of time, over the course of n days, that you and your roommate spend waiting hungrily before some food arrives. Find limn→∞ P[Sn ≤ 7n]. (b) Let Tn be the number of times, over the course of n days, that the Chinese food comes first. Find limn→∞ P[Tn ≤ .6n].

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $26,000 per month for 30 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 20 years at an estimated cost of $977,000. Third, after he passes on at the end of the 30 years of withdrawals, he would like to leave an inheritance of $550,000 to his nephew Frodo. He can afford to save $1,700 per month for the next 20 years.

If he can earn a 10 percent EAR before he retires and a 7 percent EAR after he retires, how much will he have to save each month in years 21 through 30?

bilbo baggins wants to save money to meet three objectives. first, he would like to be able to retire 30 years from now with retirement income of $23,000 per month for 20 years, with the first payment received 30 years and 1 month from now. second, he would like to purchase a cabin in rivendell in 20 years at an estimated cost of $1,034,000. third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $800,000 to his nephew frodo. he can afford to save $1,800 per month for the next 20 years. if he can earn a 10 percent ear before he retires and a 8 percent ear after he retires, how much will he have to save each month in years 21 through 30?

A box with mass m = 2.2kg on an inclined frictionless surface is released from rest from a height h = 2.35 m . After reaching the bottom of the incline the box slides with friction (coefficient of kinetic friction = 1.2) along a horizontal surface until coming to a rest after a distance d.

1. Draw a free body diagram for the box while it is on the incline. Clearly label all forces with standard names.

2. Draw a free body diagram for the box while it is on the horizontal surface. Clearly label all forces with standard names.

3. What is the kinetic energy of the box at the bottom of the incline?

4. Calculate the distance d the box will travel on the horizontal surface before coming to a rest.

5. How much is the total work done by the frictional force on the box? Explain conceptually why the work is positive or negative.

Balance Sheet Effects: Two companies, Energen and Hastings Corporation, began operations with identical balance sheets. A year later, both required additional fixed assets at a cost of $100,000. Energen obtained a 5-year, loan at an 6% interest rate from its bank. Hastings, on the other hand, decided to lease the require $100,000 capacity for 5 years, and an 6% return was built into the lease. The balance sheet for each company, before the asset increases, follows: Current assets 35,000 Debt 60,000 Fixed assets 115,000 Equity 90,000 Total assets 150,000 Total claims 150,000 a. Show the balance sheets for both firms after the asset increases, and calculate each firm's new debt ratio assuming that the lease is not capitalized. b. Show how Hastings's balance sheet would look immediately after the financing assuming the lease is capitalized.

1. Initially (before any reaction occurs) a 1.00 liter reaction vessel at 400 °C contains 0.406 moles of O₂(g) and 0.746 moles of NH₃(g) and no water or nitrogen. Consider the following:

a) If 0.071 moles of O₂(g) react, how many moles of NH₃(g) must react and how many moles of H₂O(g) and N₂(g) are formed? How many moles of O₂(g), NH₃(g), H₂O(g) and N₂(g) remain after completion of the reaction?

b) If '3x' moles of O₂(g) react, how many moles of NH₃(g) must react and how many moles of H₂O(g) and N₂(g) are formed(in terms of 'x')? How many moles of O₂(g), NH₃(g), H₂O(g) and N₂(g) remain after completion of the reaction?

The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $920,000, and it would cost another $20,000 to install it. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $500,000. The MACRS rates for the first three years are 0.3333, 0.4445, and 0.1481. The machine would require an increase in net working capital (inventory) of $15,500. The sprayer would not change revenues, but it is expected to save the firm $304,000 per year in before-tax operating costs, mainly labor. Campbell's marginal tax rate is 25%.

a. What is the Year-0 cash flow?

b. What are the cash flows in Years 1,2, and 3?

c. What is the additional Year-3 cash flow (i.e. the after-tax salvage and the return of working capital)?

d. If the projects cost of capital is 12%, what is the NPV?