5. The number of hours of daylight varies throughout the course of a year. In the Northern Hemisphere, the longest day is June 21, and the shortest is December 21. The average length of daylight is 12 h, and the variation from this average depends on the latitude. The graph below shows the number of hours of daylight at different times of the year for various latitudes. 20 18 16 14 12 Hours 10 60° N 8 50° N 40° N 30° N 4 20° N 2 Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. In Philadelphia (40°N latitude), the longest day of the year has 14 h 50 min of daylight, and the shortest day has 9 h 10 min of daylight. a. Find a sine function L that models the length of daylight as a function of t, the number of days from January 1. Explain how you determined the values of your constants. b. An astronomer needs at least 11 hours of darkness for a long exposure astronomical photograph. On what days of the year are such long exposures possible? Explain how you got your answer.
5. The number of hours of daylight varies throughout the course of a year. In the Northern Hemisphere, the longest day is June 21, and the shortest is December 21. The average length of daylight is 12 h, and the variation from this average depends on the latitude. The graph below shows the number of hours of daylight at different times of the year for various latitudes. 20 18 16 14 12 Hours 10 60° N 8 50° N 40° N 30° N 4 20° N 2 Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. In Philadelphia (40°N latitude), the longest day of the year has 14 h 50 min of daylight, and the shortest day has 9 h 10 min of daylight. a. Find a sine function L that models the length of daylight as a function of t, the number of days from January 1. Explain how you determined the values of your constants. b. An astronomer needs at least 11 hours of darkness for a long exposure astronomical photograph. On what days of the year are such long exposures possible? Explain how you got your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:5. The number of hours of daylight varies throughout the course of a year. In the Northern
Hemisphere, the longest day is June 21, and the shortest is December 21. The average length of
daylight is 12 h, and the variation from this average depends on the latitude. The graph below
shows the number of hours of daylight at different times of the year for various latitudes.
20
18
16
14
12
Hours 10
60° N
8
50°N
40° N
30°N
4
20°N
Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.
In Philadelphia (40°N latitude), the longest day of the year has 14 h 50 min of daylight, and the
shortest day has 9 h 10 min of daylight.
a. Find a sine function L that models the length of daylight as a function of t, the number of
days from January 1. Explain how you determined the values of your constants.
b. An astronomer needs at least 11 hours of darkness for a long exposure astronomical
photograph. On what days of the year are such long exposures possible? Explain how you
got your answer.
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