#$&* course Mth 277 9/9 11 &&&& query modeling exercise
.............................................
Given Solution: ** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t. If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **
.........................................
15:10:20
......!!!!!!!!...................................
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):I see here that you said ""if the circle has radius 5"" and then subtracted or added to find the units, but i didn't know if i was to ""say"" there should be a radius, or acutally find it with that given information. I understand it though ------------------------------------------------ Self-critique Rating:3
......!!!!!!!!...................................
15:22:13 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: the radius is just the distance from the origin to one of the points on a x or y axis. you can position the circle so that the radius is the same on all sides, else it wouldn't be a circle. confidence rating #$&*:2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: ** The center of the circle will be halfway between the max and min values, which can be found by averaging the two values (i.e., add and divide by 2). The diameter will be the difference between the max and min values and the radius will be half of the diameter. **
.........................................
15:22:16 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:3 &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: if we are talking in terms of days, we have a radius of 365.25/2 = 182.625 ( we will round to 183 ) so 2 pi / 365 = 0.017 cycles per day if its in weeks we have 2 pi / 52 = 0.12 cycles per week months, we have 2 pi / 12 = pi/6 or 0.52 cycles per month confidence rating #$&*:2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. If the period is in months then you have 2 pi / 12 cycles per month, or pi/6 cycles per month. The vertical coordinate of the center will be the day length midway between the min and max day lengths, which is 12 hours.**
......!!!!!!!!...................................
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ??????I wasn't very sure of what terms you wanted this in. days, months, weeks, etc.. I understand the math in the given solution, but I have no clue where or how you came up with saying that the vertical coordinate of the center will be the day lenght midway between min and max. why could the vertical lenght not be midway between the min and max of a week? or a month? or any other comparison you made here??? ------------------------------------------------ Self-critique Rating:2
.............................................
Given Solution: ** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week. The vertical coordinate of the center will be the temperature midway between the min and max temperatures.**
......!!!!!!!!...................................
15:58:33 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK ------------------------------------------------ Self-critique Rating:3 &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the tide model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: since tides come and go daily, (OHHHHH I suddenly understand the ""daylight"" model because the sun rises and falls daily, anyways back to the problem) you can go at this in two directions, with respect to time, or length in distance the tide moved from max and min ( or low and high tide ) time: take the time interval in which the tide was high, and low, and divide that by two to get an average. distance: take the distance in which the tide reached out the furthest on the beach, and the distance in which it receeded into the ocean, and divide to get the average distance traveled. confidence rating #$&*:2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: ** If you have a cycle in 10 hours then you have 2 pi rad in 10 hours, or 2 pi / 10 = pi/5 rad / hour. The vertical coordinate of the center will be the water level midway between the min and max water levels. **
.........................................
15:58:35 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I'm not far in my answer from your given solution, I didnt specify a time interval because i did not know it. but i could have given one just so i could come up with a solution. none the less i understand the concept and where you get the solution. i feel that if i had any given information aboutt this i could come up with an anwer like you did with the pi/5 rad / hr ------------------------------------------------ Self-critique Rating:3 &&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the ocean wave model? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (learning from your past given solution, lets say the waves come in at 3 waves per minute) 3 waves * 2 pi rad / minute = 6 pi radian waves / min. confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: ** The center will lie halfway between the highest and lowest levels. At 5 waves per minute the angular frequency would be 5 periods / minute * 2 pi rad / period = 10 pi rad / min. **
......!!!!!!!!...................................
......!!!!!!!!...................................
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):I see that you said 5 ""periods"" rather than waves. I'm not sure why, but my answer for the most part cooresponds with this one, other that the ""waves"" part in my solution ------------------------------------------------ Self-critique Rating:3
......!!!!!!!!...................................
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 2 pi r = 2 pi 3 revol. / second = 6 pi rev/ sec = revolution p sec. 6 pi (15 in) / sec = (90 pi ) in/sec = 283 in/sec 283 in/sec * 1ft/ 12 in = 23.6 ft/sec ( convert to miles per hr so get conversions) 5,280 ft in a mile and 3600 seconds in an hr 23.6ft / sec * 1 mile/ 5,280ft = 0.0045 miles / sec 0.0045 miles/ sec * 3,600 = 16.1 miles / hour confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: ** If 15 inches is the diameter of the wheel then the radius is 15 inches. The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec. Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So 6 pi rad / sec * 15 inches / radian = 90 pi inches / second. If you approximate this you get around 280 in/sec. This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx. A mile is 5280 ft and an hour is 3600 sec so this is 23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. ** Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.
.........................................
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):OK phew ------------------------------------------------ Self-critique Rating:3" Self-critique (if necessary): ------------------------------------------------ Self-critique rating: Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!