In this problem we analyze the phenomenon of “tailgating” in a car on a highway at high speeds. This means traveling too close behind the car ahead of you. Tailgating leads to multiple car crashes when one of the cars in a line suddenly slows down. The question we want to answer is: “How close is too close?”

To answer this question, let’s suppose you are driving on the highway at a speed of 100 kilometers an hour (a bit more than 60 mph). The car ahead of you suddenly puts on its brakes. We need to calculate a number of things: how long it takes you to respond; how far you travel in that time; how far the other car traveled in that time.

A. First let’s estimate how long it takes you to respond. Two times are involved: how long it takes from the time you notice something happening till you start to move to the brake, and how long it takes to move your foot to the brake.

You will need a ruler to do this. Take the ruler and have a friend hold it from the one end hanging straight down. Place your thumb and forefinger opposite the bottom of the ruler. Have your friend release the ruler suddenly and try to catch it with your thumb and forefinger. Measure how far it fell (in meters) before you caught it. Do this three times and take the average distance — we will call this r. Assuming the ruler was falling freely without air resistance, you can calculate how much time it took before you caught it, t1, using the equation r = (5 m/s2) * t12.

Also, you can estimate the time, t2, it takes you to move your foot from the gas pedal to the brake pedal. Your total reaction time is t1 + t2.

What was your t1?

1 s

What was your estimate for t2?

2 s

So what is your reaction time? (Use your estimates.)

3 s

B. If you brake hard and fast, you can bring a typical car to rest from 100 kph (about 60 mph) in 5 seconds.

B.1 Calculate the magnitude of your acceleration, −a0, assuming that it is constant.

4 m/s2

Why did we put a minus sign in front?

5This answer has not been graded yet.

B.2 Suppose the car ahead of you (which was also going 100 kph) begins to brake with an acceleration −a0 from B1. How far will he travel before he comes to a stop? (Hint: How much time will it take him to stop?)

6 m

B.3 What will be his average velocity over this time interval?

7 m/s

C. Now we can put these results together into a semi-realistic situation. You are driving on the highway at 100 km/hr and there is a car in front of you going at the same speed.

C.1 You see him start to brake immediately. (An unreasonable but temporarily useful simplifying assumption.) If you are also traveling 100 kph, how far (in meters) do you travel before you begin to brake, using your reaction time from part A.

Minimum distance = 8 m

If you can also produce the acceleration −a0 from part B1 when you brake, what will be the total distance you travel before you come to a stop?

9 m

C.2 If you don’t notice the car ahead of you beginning to brake for 1 second, how much additional distance will you travel?

10 m

C.3 On the basis of these calculations, what do you think is a safe distance to stay behind a car at 60 mph? Express your distance in “car lengths” (about 15 feet).

11 car lengths

 

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In this problem, Show that given n red points and n blue points in the plane such that no three points lie on a common line, it is possible to draw line segments between red-blue pairs so that all the pairs are matched and none of the line segments intersect. Assume that there are n red and n blue points fixed in the plane.

A matching M is a collection of n line segments connecting distinct red-blue pairs. The total length of a matching M is the sum of the lengths of the line segments in M. Say that a matching M is minimal if there is no matching with a smaller total length.

Let IsMinimal(M) be the predicate that is true precisely when M is a minimal matching. Let HasCrossing(M) be the predicate that is true precisely when there are two line segments in M that cross each other. Give an argument in English explaining why there must be at least one matching M so that IsMinimal(M) is true, i.e.

∃MIsMinimal(M)

Give an argument in English explaining why

∀M(HasCrossing(M) → ¬IsMinimal(M))

Now use the two results above to give a proof of the statement: ∃M¬HasCrossing(M). 

 

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Hello Sir

i need your help about this question:

In this thread, will discuss the concept of Linked Decisions and a decision situation that is involved in the process. With a linked decision , a selected alternative will often impact several other areas that need to be considered before the initial decision is made. This chain reaction is classified as a linked decision. As a simplistic example—with the initial decision of accepting a job in Denver over a job in Cleveland and Dallas, the linked decision would be determining which section of Denver to live in. How might you derive at your decision? What processing might you engage to determine the best alternative Dr. Daniels

Running Head: LINKED DECISIONS 1 Linked Decisions Institution AffiliatedDate LINKED DECISIONS IntroductionDecision making refer to the process of identifying and choosing the alternatives…

 

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In this thread, I would like you to comment on the nature of light and how operation of telescopes. Light has a duality of a particle and a wave; which one affects your life? Also, how does light interact with optics inside telescopic systems? Please answer these questions in two paragraphs.

 

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In this thread, discuss how Fielding develops characters in the novel. As you go through the novel, write down your insights into or about the characters.

Choose one character to discuss, but you should tie the character to the development of an idea. For example, using a specific character, explain how the character can represent such issues as male versus female characters, upper versus lower classes, the development of the arc of the character, the plausibility of characters, the use of names and/or dialogue, etc. You can consider the narrator in the novel as a character. Be sure to discuss the character from start to finish, i.e., if you choose Joseph Andrews, you have to discuss him throughout the entire novel, not just the first chapters.

Let’s see if we can determine some sort of working view towards Fielding’s use of characters.

Plot

Discuss Fielding’s use of plot in the novel. For example, you could discuss whether the plot is plausible, or not.

You may have to bring in some discussion of character, for the plot cannot move forward without the characters also moving forward. Be sure to discuss the entirety of the novel.

Setting

Focus on Fielding’s use of setting in the novel.

Watt notes that it was extremely important for the novel to reflect the contemporary scene of the novelist and the reader.

How does Fielding use the setting to make his novel more plausible to the reader? Are there any places where the novel may be hindered by the setting?

 

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