Day Length Web Activity

Transcription

1 Day Length We Activity SAMPLE Name: Follow the directions for each section and type your answers on a separate sheet of paper. Use TI-Graph Link or TI Inter Active! to present your data and models you find. Before You Begin: Do some days of the year have longer daylight hours then others? Yes. When are the days shortest and longest during the year? The days are longer during the summer and shorter during the winter. What day is the longest? What day is the shortest? The first day of summer is the longest day, June 21 st and the first day of winter, Decemer 21 st is the longest. Would Mexico and Alaska have the same hours of the day on the shortest and longest days of the year? Why or why not? No, ecause Mexico is close to the equator, so the day length etween the longest and the shortest days in Mexico varies very little compared to Alaska. Alaska is really far from the equator, so the longest day would e very long, 24 hours and the shortest day very short, asically nonexistent. What is the average length of daylight hours in a year?. Is there a day of the year when the amount of daylight is the same for everyone? If so when and how long is the day? March 22 nd and Septemer 22 nd are the two days of the year when the day length is for everyone. If you were to draw a graph representing the length of daylight hours for any given day of the year what would it look like? It would look like a sine curve with a vertical shift of 12, a period of days and a phase shift of around 80, which is when the day length is long. The amplitude would e the maximum day length, depending on the location, minus 12. What do you think would happen to your graph if you moved closer or farther from the equator? The amplitude or the height of the curve would e lower as you move toward the equator and higher as you move farther from the equator. All the cities you looked at were in the Northern Hemisphere. What do you think the graph for Australia would look like? Explain or draw your guess elow. I think that it would e like the other graphs, only the amplitude would e different and it would e upside down since their winter and summer are flipped with the seasons in the Northern Hemisphere. Created y Jana Henry page 1 of 5

2 Directions: Go to For each city, find the length of day light hours for the 7 th, 14 th and 21 st of each month and fill in the tale. Use the we search directions it see how to collect data. Enter in the days of the year into L1 in your calculator. Press, Í and then enter in the days of the year, pressing Í after each entry (column 2 on your chart). Enter in the length of the daylight hours into L2, L3 and L4 (The data given is in hours and minutes. Be sure to change the data to decimal form). To go from column to column press the ~, keys. Graph a scatter plot for each city (i.e., L1 and L2, L1 and L3, L1 and L4). Press yo. The first plot graph should e turned on, plotting L1 and L2. The second should e on plotting L1 and L3. The third plot graph again should e turned on plotting L1 and L4. To turn the plot graph on, move the curser up or down to select the numer of the scatter plot you wish to turn on. Then press Í. Press Í again to turn it on (this will highlight the word On). To change the lists, move the curser down to where it says Xlist: L1. The Xlist should always e L1 for all three graphs. If it is not, move the curser to highlight the list numer you want to change and then press y, À for L1. To change the Ylist, highlight the list you wish to change and press y then Á for L2, Â for L3 or for L4. To view your scatter graphs, press q and scroll down to 9:ZoomStat. Highlight and press Í. Enter in the length of the daylight hours into L2, L3 and L4 (The data given is in hours and minutes. Be sure to change the data to decimal form) Graph a scatter plot for each city (i.e., L1 and L2, L1 and L3, L1 and L4) Find y = Acos(B( x C ) + D and y = Asin(B( x C ) + D that models the data for each city. (Show and explain calculations) Analysis: What is the same and what is different in terms of A, B, C and D? I noticed that B, C, and D are the same for all of the curves - The only thing that changes is A. Part II: Find y = Acos(B( x C) + D and y = Asin(B( x C ) + D ) that models the data for each city. What is your explanation as to why they are the same or different? It makes sense that A is different etween the three curves, since it affects the amplitude or height of the curve - that was the only thing that was different etween them. The closer the location is to equator the lower the amplitude. I noticed that D was around 12 in all the graphs, which is the average length of a day in a year. It was not hard to realize why B was the same for all the graphs. They all have the same period since one cycle is complete in days. When finding the sine for the graphs the horizontal shift was at first day of the year that had of daylight. This was aout the 81 st day for all the curves, which is March 22 nd the spring equinox. Created y Jana Henry page 2 of 5

3 Day Day of the Year San Francisco California Montreal Canada Length of Daylight Anchorage Alaska Shanghai China Sydney Australia Honolulu Hawaii Jan Jan Jan Fe Fe Fe Mar Mar Mar Apr Apr Apr May May May Jun Jun Jun Jul Jul Jul Aug Aug Aug Sep Sep Sep Oct Oct Oct Nov Nov Nov Dec Dec Dec Equations for Part II: San Francisco: Shanghai: Montreal: Sydney: Anchorage: Honolulu: Created y Jana Henry page 3 of 5

4 Created y Jana Henry 5/30/2002 San Francisco, California: Looking at the data, I found the highest point changed from (c) = 2.49 = = The final sine function is y = 2.49sin ( x 80) Hours. The cosine curve is the same only it s negative and with a phase shift of negative 10, which means that, the graph would start on Decemer 22, when it has a length of. y = 2.49 cos ( x + 10) when y= This day. Therefore, c=80. Montreal, Canada: Looking at the data, I found the highest point = when y= This changed from (c). = = 3.35 The final sine function is y = 3.35sin ( x 80) The cosine curve is the same only it s negative and c = -10, y = 3.35cos ( x + 10) Anchorage, Alaska: Looking at the data, I found the highest point = when y= This changed from (c). = = 6.66 The final sine function is y = 6.66sin ( x - 80) The cosine curve is the same only it s negative and c = -10, y = 6.66cos ( x +10) Created y Jana Henry page 4 of 5

5 Honolulu, Hawaii: Looking at the data, I found the highest point = when y= This changed from (c). = = 1.25 The final sine function is y = 1.25sin ( x - 80) The cosine curve is the same only it s negative and c = -10, y = 6.66cos ( x +10) Shanghai, China: Looking at the data, I found the highest point = when y= This changed from (c). = = 1.97 The final sine function is y = 1.97sin ( x - 80) The cosine curve is the same only it s negative and c = -10, y = 1.97cos ( x +10) Sydney, Australia: Looking at the data, I found the highest point = when y= This changed from (c). = The fall equinox = 2.19 The final sine function is y = 2.19sin ( x - 80) The cosine curve is the same only it s positive and c = -10, y = 2.19cos ( x +10) Created y Jana Henry page 5 of 5