query 2

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

002. `ph1 query 2

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Question: Explain how velocity is defined in terms of rates of change.

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Your solution: Velocity is the measurement of change of something over the change of something in reference to time. Such as velocity is the measurement of change of a marble rolling down a ramp and how long it takes to get to the end.

Confidence rating: I know, it’s difficult to put in words.

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Given Solution: Average velocity is defined as the average rate of change of position with respect to clock time.

The average rate of change of A with respect to B is (change in A) / (change in B).

Thus the average rate of change of position with respect to clock time is

• ave rate = (change in position) / (change in clock time).

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Self-critique (if necessary): My definition needs more clarity.

Self-critique Rating: 2

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Question: Why can it not be said that average velocity = position / clock time?

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Your solution: It can not be said that average velocity = position/clock time because position is the measurement on one place, where average velocity is the rate of change in many places along the same continuum during a certain amount of time.

Confidence rating: 3

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Given Solution: The definition of average rate involves the change in one quantity, and the change in another.

Both position and clock time are measured with respect to some reference value. For example, position might be measured relative to the starting line for a race, or it might be measured relative to the entrance to the stadium. Clock time might be measure relative to the sound of the starting gun, or it might be measured relative to noon.

So position / clock time might, at some point of a short race, be 500 meters / 4 hours (e.g., 500 meters from the entrance to the stadium and 4 hours past noon). The quantity (position / clock time) tells you nothing about the race.

There is a big difference between (position) / (clock time) and (change in position) / (change in clock time).

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Self-critique (if necessary): I think we’re both trying to say the same thing just in different ways.

Self-critique Rating: 2

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Question: Give your solution to the following, which should be in your notes: Find the approximate uncertainty in the area of a circle given that its radius is 2.8 * 10^4 cm.

STUDENT COMMENT: When finding approximate uncertainty, the number is rounded to one significant number and its power of 10. With this in mind, the radius 2.8 * 10^4 could in actuality be 2.85 * 10^4 or 2.745 *10^4 , if we stay within the same power of 10.

Area of a circle pi* r^2 = 3.1415 * (2.85 * 10^4)^2 = 8.95 * 10^8

= 3.1415 * (2.745 * 10^4)^2 = 8.262 * 10^8

INSTRUCTOR RESPONSE:

The key is the first sentence of the given solution:

'Radius 2.8 * 10^4 cm means that the radius is between 2.75 * 10^4 cm and 2.85 * 10^4 cm.'

You know this because you know that any number which is at least 2.75, and less than 2.85, rounds to 2.8.

Ignoring the 10^4 for the moment, and concentrating only on the 2.8:

Since the given number is 2.8, with only two significant figures, all you know is that when rounded to two significant figures the quantity is 2.8. So all you know is that it's between 2.75 and 2.85.

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Your solution:

When finding approximate uncertainty, the number is rounded to one significant number and its power of 10. With this in mind, the radius 2.8 * 10^4 could in actuality be 2.85 * 10^4 or 2.745 *10^4 , if we stay within the same power of 10.

Area of a circle pi* r^2 = 3.1415 * (2.85 * 10^4)^2 = 2.55 * 10^9

= 3.1415 * (2.75 * 10^4)^2 = 2.38 * 10^9

3.1415 * (2.8 * 10^4)^2 = 2.46 * 10^9

Confidence rating: Not sure.

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Given Solution:

** Radius 2.8 * 10^4 cm means that the radius is between 2.75 * 10^4 cm and 2.85 * 10^4 cm.

This means that the area is between pi * (2.75 * 10^4 cm)^2 = 2.376 * 10^9 cm^2 and pi * (2.85 * 10^4 cm)^2 = 2.552 * 10^9 cm^2. The difference is .176 * 10^9 cm^2 = 1.76 * 10^8 cm^2, which is the uncertainty in the area.

Note that the .1 * 10^4 cm uncertainty in radius is about 4% of the radius, which the .176 * 10^9 cm uncertainty in area is about 8% of the area. This is because the area is proportional to the squared radius. A small percent uncertainty in the radius gives very nearly double the percent uncertainty in the squared radius. **

Self-critique (if necessary):

The Order of operations almost caught me. Uncertainty estimates take time to prove.

Self-critique Rating:

2. Now I understand this problem.

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Question: What is your own height in meters and what is your own mass in kg? Explain how you determined these? What are your uncertainty estimates for these quantities, and on what did you base these estimates?

Your solution:

My height: 68 inches * 1 m / 39.37 inches = 1.73 m

My mass: 199 lb * 1 kg / 2.2 lb = 90.46 kg

The uncertainty estimates for my height 1.73 +or- .01

The uncertainty estimate for my mass in 90.46 +or- .01

My actual height must lie somewhere between 1.72m and 1.74 m. My actual mass must be between 90.45kg and 90.47kg.

Confidence rating:

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Given Solution:

Presumably you know your height in feet and inches, and have an idea of your ideal weight in pounds. Presumably also, you can convert your height in feet and inches to inches.

To get your height in meters, you would first convert your height in inches to cm, using the fact that 1 inch = 2.54 cm. Dividing both sides of 1 in = 2.54 cm by either 1 in or 2.54 cm tells us that 1 = 1 in / 2.54 cm or that 1 = 2.54 cm / 1 in, so any quantity can be multiplied by 1 in / (2.54 cm) or by 2.54 cm / (1 in) without changing its value.

Thus if you multiply your height in inches by 2.54 cm / (1 in), you will get your height in cm. For example if your height is 69 in, your height in cm will be 69 in * 2.54 cm / (1 in) = 175 in * cm / in.

in * cm / in = (in / in) * cm = 1 * cm = cm, so our calculation comes out 175 cm.

STUDENT SOLUTION

5 feet times 12 inches in a feet plus six inches = 66 inches. 66inches * 2.54 cm/inch = 168.64 cm. 168.64 cm *

.01m/cm = 1.6764 meters.

INSTRUCTOR COMMENT:

Good, but note that 66 inches indicates any height between 65.5 and 66.5 inches, with a resulting uncertainty of about .7%.

168.64 implies an uncertainty of about .007%.

It's not possible to increase precision by converting units.

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Self-critique (if necessary):

I did the conversions correctly, but I’m not sure about the Uncertainty analysis.

Self-critique Rating: 2

query 2

&#Your work looks good. Let me know if you have any questions. &#