A pair of bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear, as seen in part (a) of the figure below. ((a) before collision, (b) after collision) One has a mass of m1 = 462 kg and the other m2 = 546 kg, owing to differences in passenger mass. If the lighter one approaches at v1 = 4.48 m/s and the other is moving at v2 = 3.63 m/s, calculate the velocity of the lighter car after the collision.

Calculate the velocity of the heavier car after the collision.

Calculate the change in momentum of the lighter car.

Calculate the change in momentum of the heavier car.

(a) Have you ever visited an amusement park and taken a ride on a parachute drop ride? These types of rides take the passengers to a great height, and then drop them in free fall. Before they hit the ground, the ride is slowed using a Lenz’s law mechanism thus avoiding certain death. For this discussion, first locate a photo of one of these rides (either one you’ve personally experienced or one you might like to try someday), and in your initial post, upload the photo and respond to the following:

• Explain how Lenz’s law applies to this situation.
• Why is the Lenz’s law mechanism ideal for such a use?
• What other mechanisms can be used to slow the descent? Compare and contrast these options with the Lenz’s law mechanism.

(b) As you have learned, an electromagnet is a magnet that is produced by electric current. Think about how electromagnets are used and what you have seen or heard of them being used for. In your initial discussion post, respond to the following:

• Which of the principles or laws discussed in this module explain how an electromagnet works?
• Describe in detail two modern applications of electromagnets. Do these electromagnets draw a large amount of current or a little? How do you know? What supplies that current?
• Why do you think electromagnets are used in these different ways?
• What is the advantage of using an electromagnet rather than a permanent magnet?

a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it. Can the equation for conservation of mechanical energy be used on the child?

YesNo     

(b) Is the mass of the child a factor in determining his speed at the bottom of the slide?

YesNo     

(c) The child drops straight down rather than following the curved ramp of the slide. In which case will he be traveling faster at ground level?

following the curved rampdropping straight down     same speed in either case

(d) If friction is present, how would the conservation-of-energy equation be modified?


(e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 13.5 m. (Assume the child is initially at rest.)
m/s

Water Planet is considering purchasing a water park in Miami, Florida​, for $ 2,100,000. The new facility will generate annual net cash inflows of $ 535,000 for eight years. Engineers estimate that the facility will remain useful for eight years and have no residual value. The company uses​ straight-line depreciation. Its owners want payback in less than five years and an ARR of 10​% or more. Management uses a 12% hurdle rate on investments of this nature.

.

Requirement 1. Compute the payback​ period, the​ ARR, the​ NPV, and the approximate IRR of this investment.​ (If you use the tables to compute the​ IRR, answer with the closest interest rate shown in the​ tables.) ​(Round the payback period to one decimal​ place.)

​(Round the percentage to the nearest tenth​ percent.)

​(Round your answer to the nearest whole​ dollar.)

The IRR​ (internal rate of​ return) is between

.

Requirement 2. Recommend whether the company should invest in this project.

an insurance company crashed four cars in succession at 5 miles per hour. the cost of repair of the four crashes was $429 $459 $318. Compute the range, sample variance, and sample standard deviation cost of repairs

2. For each of the following variables, indicate if it is quantitative or categorical and also indicate the scale of measurement used for each:

The Gender of an individual

The Weight(pounds) of a package

The Income(dollars) of an individual

The Distance(miles) between two cities

Suppose the federal government is considering requiring all new trucks to meet a new higher efficiency standard of 50 miles per gallon. Give an example of a cost and a benefit that might arise from this policy change.

A contractor plans to use a wheeled loader to move 5,000 BCY of soil 500 feet using a 50-minute working hour. The soil has a swell of 15%. The loader has a bucket capacity of 2.5 cubic yards. The soil has a fill factor of 1.2 and a weight of 2,500 lbs per LCY. The loader has an STL of 50% of 15,000 lbs. The loader will haul in one direction loaded at 2.5 miles per hour and return at 3.5 miles per hour. The total cost of the tractor is $55.00 per hour.  It has a fixed time of .35 minutes. Remember that the loader will be moving the dirt in its loose state. How many days will it take to move all of the dirt working 8 hours per day?