Three particles A, B, and C with masses mA=2mB=mC are arranged (in that order) in a straight line. Initially, B and C are at rest a distance L apart, and A is projected towards B with speed vA. The particles then undergo elastic head‐on collisions.

SHOW THAT:

a)for any elastic head‐on collision, the relative speed of the two objects after the collision has the same magnitude (but opposite direction) as before the collision: ? vA-vB=-(v_fA-v_fB) ... (f for final/after collision)

b)A and B collide twice and that the time interval between these two collisions is ∆?t=12L/7vA

A 110-kg rugby player is sliding on a muddy field at a speed of 2 m/s toward the right as a 82-kg player is slipping at a speed of 3 m/s toward the left. As the two players collide, they grab onto each other and slide away together as one.

What kind of collision was this?

Set up the conservation of linear momentum for this collision, and determine the shared velocity (magnitude & direction) of the players immediately after the collision.

Would the players' total kinetic energy before the collision be equal to their total kinetic energy after? yes/no

A $250,000 mortgage was originally financed at 8% annual interest over 30 years with monthly payments and compounding. After making your final payment in year 5, interest rates have fallen to 4% and you are considering refinancing.

What is your monthly mortgage payment under the initial loan?

What would be your new monthly mortgage payment after refinancing?

If the refinancing cost is 2% of the remaining balance on your loan, how much longer would you need to remain in your house before refinancing paid itself off?

36. Point-of-service (POS) plans are similar to those offered by planned provider organizations (PPOs), yet they allow for consumers to select non-plan providers when seeking medical care. Those who choose non-plan providers, however, will be expected to: Select one:

a. Contribute a large percentage of the copayment

b. Excuse themselves from the POS plan after medical services have been received

c. Pay large deductibles on their medical bills before the insurer picks up the bill

d. Pay higher premiums after receiving services.

A company is considering the purchase of an industrial laser for $150,000. The device has a useful life of five years and a salvage (market) value of $30,000 at the end of those five years. The before-tax cash flow is estimated to be $45,000 per year. The laser would be depreciated using MACRS with a recovery period of three years. If the effective income tax is 25% and the after-tax MARR is 15%, use the PW method on an after-tax basis to determine the profitability of the laser and make a recommendation.

** Please do the math by hand and NOT using Excel, thank you.

Particle A of mass m, initial velocity 20i (m/s) has a collision with a stationary particle B of mass 2m. After collision, VA(final)=10i+5j (m/s). a) Find VB(final) if the system (particle A plus B) linear momentum is conserved (both i and j directions). What are the velocities of center of the system before and after collision?b) Find the system’s % KE lost due to the collision (m=20.0gram). c) If the collision time between A and B is 0.050 s, what is the average force between A and B during the collision?

A construction company plans to invest in new equipment to improve their productivity. The planned investment is $500,000 now and $100,000 in year 1. The gross income for year 1 is $175,000, year 2 is $300,000, and year 3 is $600,000. Taxes related to the investment are $50,000 in year 1, $75,000 in year 2 and $100,000 in year 3.

Determine:

a) The before tax rate of return for the investment

b) The after-tax rate of return for the investment

c) How does the after-tax rate of return compare to the company’s MARR of 15%?

Please do not use excel

1) A projectile has the least speed at what point in its path?

a) At its maximum height.

b) Just before it hits the ground.

c) Just after it's fired.

d) After three seconds of travel.

2) The magnitude of a vector can never equal the length of one of its components.

True

False

3) Can a particle with a constant speed ever be accelerating?

a) Yes, because acceleration and velocity are unrelated.

b) No, because its speed is constant.

c) Yes, because it's speed is changing.

d) Yes, if it's changing direction.

In a study to assess the effectiveness of garlic for lowering cholesterol, 50 adults were treated with garlic tablets. Cholesterol levels were measured before and after treatment. The changes in their LDL cholesterol (in mg/dL) have a mean of 8 and a standard deviation of 4. (a) Construct a 95% interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment. (Round the lower bound and upper bound of the confidence interval to two decimal places) Include description of how confidence interval was constructed. (b) Describe the results of the study in everyday language.