course Phy 241
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19:52:11 `q001. It will be very important in this course for your instructor to see and understand the process of visualization and reasoning you use when you solve problems. This exercise is designed to give you a first experience with these ideas, and your instructor a first look at your work. Answer the following questions and explain in commonsense terms why your answer makes sense.
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RESPONSE -->
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19:52:25 For each question draw a picture to make sense out of the situation, and include a description of the picture. Samples Sample question and response Question: If a bundle of shingles covers 30 square feet, how many bundles are required to cover a 600 square foot roof? Response: We might draw a picture of a rectangle representing the area, dividing the rectangle into a number of smaller rectangles each representing the area covered by a single bundle. This makes it clear that we are dividing the roof area into 1-bundle areas, and makes it clear why we are going to have to divide. Reasoning this problem out in words, we can say that a single bundle would cover 30 square feet. Two bundles would cover 60 square feet. Three bundles would cover 90 square feet. We could continue in this manner until we reach 600 square feet. However, this would be cumbersome. It is more efficient to use the ideas of multiplication and division. We imagine grouping the 600 square feet into 30 square foot patches. There will be 600 / 30 patches and each will require exactly one bundle. We therefore require 600 / 30 bundles = 20 bundles. {}Your responses might not be as clear as the above, though they might be even more clear. I won't be looking for perfection, though I wouldn't object to it, but for a first effort at visualizing a situation and communicating a reasoning process. This is not something you are used to doing and it might take a few attempts before you can achieve good results, but you will get better every time you try. {}You might be unsure of what to do on a specific question. In such a case specific questions and expressions of confusion are also acceptable responses. Such a response must include your attempts to come up with a picture and reason out an explanation. For example your response might be Sample expression of confusion: I've drawn a picture of a pile of bundles and a roof but I'm not sure how to connect the two. I tried multiplying the number of bundles by the square feet of the roof but I got 18,000, and I know it won't take 18,000 bundles to cover the roof. How do you put the area covered by a bundle together with the roof area to get the number of bundles required? A poor response would be something like 'I don't know how to do #17'. This response reveals nothing of your attempt to understand the question and the situation. Nor does it ask a specific question. Incidentally, you might be tempted to quote rules or formulas about rates and velocities in answering these questions. Don't. This exercise isn't about being able to memorize rules and quote them. It is about expanding your ability to visualize, reason and communicate.
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RESPONSE --> OK
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19:53:51 In your own words briefly summarize the instructions and the intent of this exercise.
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RESPONSE --> The purpose of these exercises is to get the student using common sense when answering questions. Analyze the question by drawing a picture of what it's asking you and solve the problem using that picture. Don't just quote formulas or rules to come up with an answer. Explain in writing what you see in that picture so the instructor can see if you understand or not understand.
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19:54:55 `q001. If you earn 50 dollars in 5 hours, at what average rate are you earning money, in dollars per hour?
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RESPONSE --> In order to find the answer to this problem I would divide the number of dollars earned by the number of hours worked to find my hourly rate. 50 dollars / 5 hours = 10 dollars per hour
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19:55:27 If you travel 300 miles in 6 hours, at what average rate are you traveling, in miles per hour?
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RESPONSE --> I would divide the miles driven by the number of hours driven and this will give me the rate I am traveling in miles per hour. 300 miles driven / 6 hours driven = 50 mi / hr
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19:56:07 `q002. If a ball rolling down a grooved track travels 40 centimeters in 5 seconds, at what average rate is the ball moving, in centimeters per second?
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RESPONSE --> In order to find to find the answer in centimeters per second, we could take 40 centimeters and divide it by 5 seconds. This would give you 8 centimeters per second.
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19:56:38 The preceding three questions illustrate the concept of a rate. In each case, to find the rate we divided the change in some quantity (the number of dollars or the distance, in these examples) by the time required for the change (the number of hours or seconds, in these examples). Explain in your own words what is meant by the idea of a rate.
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RESPONSE --> Rate can be seen as a ratio of a part of something with respect to a whole of something ie, (an amount of distance per unit of time ).
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19:57:08 `q003. If you are earning money at the average rate of 15 dollars per hour, how much do you earn in 6 hours?
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RESPONSE --> In this example, to see how much total money you can make, take the average rate and multiply by the total hrs worked. 15 (dollars/hr) * 6 hr = 90 dollars
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19:57:37 If you are traveling at an average rate of 60 miles per hour, how far do you travel in 9 hours?
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RESPONSE --> To find total miles driven take the average rate and multiply it by total hrs driven. 60 (mi/hr) * 9 hrs. = 540 miles
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19:58:50 `q004. If a ball travels at and average rate of 13 centimeters per second, how far does it travel in 3 seconds?
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RESPONSE --> If you take the average rate and multiplied by the total time the ball travels this will tell you how far the ball traveled. 13 (centimeters / sec) * 3 sec = 39 centimeters
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19:59:17 In the preceding three exercises you turned the concept of a rate around. You were given the rate and the change in the clock time, and you calculated the change in the quantity. Explain in your own words how this increases your understanding of the concept of a rate.
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RESPONSE --> In these examples you're given a total of time and the rate of distance to time and asked to find the total distance.
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20:00:59 `q005. How long does it take to earn 100 dollars at an average rate of 4 dollars per hour?
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RESPONSE --> To find the amount of time it would take to earn a total of 100 dollars, one must divide the total by the rate. In this case 100 dollars / 4 (dollars / hr) = 25 hrs to earn 100 dollars.
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20:01:38 How long does it take to travel 500 miles at an average rate of 25 miles per hour?
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RESPONSE --> Again, same case as above, take the total and divide by the rate. 500 miles / 25 (miles/hr) = 20 hrs.
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20:02:01 `q006. How long does it take a rolling ball to travel 80 centimeters at an average rate of 16 centimeters per second?
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RESPONSE --> 80 centimeters / 16 ( centimeters / sec ) = 5 sec.
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20:02:45 In the preceding three exercises you again expanded your concept of the idea of a rate. Explain how these problems illustrate the concept of a rate.
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RESPONSE --> In the 3 above examples we are given the total of distance and the rate of (distance to time) and asked to find the total time.
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