draw a picture, then label the picture, then state what you know and the assumpt
ID: 1536596 • Letter: D
Question
draw a picture, then label the picture, then state what you know and the assumptions you are making, then describe the steps you will take to make the estimate, and then get an answer.Try to use the powers of 10 notation.
1- Estimate the number of piano tuners in New York City. This estimation problem is similar to the problem of the number of barbers who cut men's hair in Brooklyn. Hints: * How many households in New York? This can be estimated by the population of New York divided by say 4.
* How many households have pianos? Try to guess based on you knowledge of going to friends and relative homes.
* How often is a piano tuned in say a year?
* How long does it take to tune a piano? Thus you should be able to estimate the number of pianos that a single piano tuner can tune in a year.
2- The nearest star to the earth, Proxima Centuri, is 4.3 light years away. Suppose a rocket ship is sent directly from the earth to the nearest star with a constant speed of 10 miles per second (east coast to the west coast in less than 5 minutes). How many years would it take to reach the nearest star? In a previous homework you calculated the approximate distance of a light year knowing that light travels at 186,000 miles in a second and a year has approximately 3x10^7 seconds.
3- One can find the phases of the moon from 1951 through 2017 on the following site:
http://stardate.org/nightsky/moon
or from 1930 to 2026 on the following site:
http://www.moonconnection.com/moon_phases_calendar.phtml
3A- The definition of Easter Sunday from looking at the behavior of the earth and moon is as follows:
* Wait for the Spring Equinox (usually March 20 or 21) * Then wait for the first full moon after the Equinox. * Then, the Sunday after the full moon is Easter Sunday!
Find Easter Sunday for the years 1951 and separately 2015 using one of the web sites above. Also for each year, 1951 and 2015, what is the approximate date (month, day of week, and date) of the full moon after the Spring Equinox? (This is the start date for Passover.) Check on a search engine if the dates you determined for Easter Sunday and Passover for 1951 and 2015 are correct.
3B- There is an accidental astronomical relationship between the two main calendars in use today, the solar calendar and the lunar calendar.
The calendar is based on three key astronomical events.â—¾ * A day, which is the time from one sunrise to the next sunrise - one complete rotation of the Earth. * A calendar year, which is approximately 365.2425 days - one complete orbit of Earth around the Sun. * A lunar month, which is approximately 29.53059 days - one complete orbit of the Moon around the Earth.
Multiply 19 solar calendar years by the number of days in a year. (Multiply 19 x 365.2425). Show that the number you obtain is almost exactly equals the same total number of days in 235 lunar months. (Multiply 235 x 29.53058).
3C- From the moon sites above, find the status (shape) of the moon on your birthdate in 2017. Also find the shape of the moon on your birthdate 19 years earlier (in 1998). What was the shape of the moon on each of those dates and why are the two very closely the same? draw a picture, then label the picture, then state what you know and the assumptions you are making, then describe the steps you will take to make the estimate, and then get an answer.
Try to use the powers of 10 notation.
1- Estimate the number of piano tuners in New York City. This estimation problem is similar to the problem of the number of barbers who cut men's hair in Brooklyn. Hints: * How many households in New York? This can be estimated by the population of New York divided by say 4.
* How many households have pianos? Try to guess based on you knowledge of going to friends and relative homes.
* How often is a piano tuned in say a year?
* How long does it take to tune a piano? Thus you should be able to estimate the number of pianos that a single piano tuner can tune in a year.
2- The nearest star to the earth, Proxima Centuri, is 4.3 light years away. Suppose a rocket ship is sent directly from the earth to the nearest star with a constant speed of 10 miles per second (east coast to the west coast in less than 5 minutes). How many years would it take to reach the nearest star? In a previous homework you calculated the approximate distance of a light year knowing that light travels at 186,000 miles in a second and a year has approximately 3x10^7 seconds.
3- One can find the phases of the moon from 1951 through 2017 on the following site:
http://stardate.org/nightsky/moon
or from 1930 to 2026 on the following site:
http://www.moonconnection.com/moon_phases_calendar.phtml
3A- The definition of Easter Sunday from looking at the behavior of the earth and moon is as follows:
* Wait for the Spring Equinox (usually March 20 or 21) * Then wait for the first full moon after the Equinox. * Then, the Sunday after the full moon is Easter Sunday!
Find Easter Sunday for the years 1951 and separately 2015 using one of the web sites above. Also for each year, 1951 and 2015, what is the approximate date (month, day of week, and date) of the full moon after the Spring Equinox? (This is the start date for Passover.) Check on a search engine if the dates you determined for Easter Sunday and Passover for 1951 and 2015 are correct.
3B- There is an accidental astronomical relationship between the two main calendars in use today, the solar calendar and the lunar calendar.
The calendar is based on three key astronomical events.â—¾ * A day, which is the time from one sunrise to the next sunrise - one complete rotation of the Earth. * A calendar year, which is approximately 365.2425 days - one complete orbit of Earth around the Sun. * A lunar month, which is approximately 29.53059 days - one complete orbit of the Moon around the Earth.
Multiply 19 solar calendar years by the number of days in a year. (Multiply 19 x 365.2425). Show that the number you obtain is almost exactly equals the same total number of days in 235 lunar months. (Multiply 235 x 29.53058).
3C- From the moon sites above, find the status (shape) of the moon on your birthdate in 2017. Also find the shape of the moon on your birthdate 19 years earlier (in 1998). What was the shape of the moon on each of those dates and why are the two very closely the same? draw a picture, then label the picture, then state what you know and the assumptions you are making, then describe the steps you will take to make the estimate, and then get an answer.
Try to use the powers of 10 notation.
1- Estimate the number of piano tuners in New York City. This estimation problem is similar to the problem of the number of barbers who cut men's hair in Brooklyn. Hints: * How many households in New York? This can be estimated by the population of New York divided by say 4.
* How many households have pianos? Try to guess based on you knowledge of going to friends and relative homes.
* How often is a piano tuned in say a year?
* How long does it take to tune a piano? Thus you should be able to estimate the number of pianos that a single piano tuner can tune in a year.
2- The nearest star to the earth, Proxima Centuri, is 4.3 light years away. Suppose a rocket ship is sent directly from the earth to the nearest star with a constant speed of 10 miles per second (east coast to the west coast in less than 5 minutes). How many years would it take to reach the nearest star? In a previous homework you calculated the approximate distance of a light year knowing that light travels at 186,000 miles in a second and a year has approximately 3x10^7 seconds.
3- One can find the phases of the moon from 1951 through 2017 on the following site:
http://stardate.org/nightsky/moon
or from 1930 to 2026 on the following site:
http://www.moonconnection.com/moon_phases_calendar.phtml
3A- The definition of Easter Sunday from looking at the behavior of the earth and moon is as follows:
* Wait for the Spring Equinox (usually March 20 or 21) * Then wait for the first full moon after the Equinox. * Then, the Sunday after the full moon is Easter Sunday!
Find Easter Sunday for the years 1951 and separately 2015 using one of the web sites above. Also for each year, 1951 and 2015, what is the approximate date (month, day of week, and date) of the full moon after the Spring Equinox? (This is the start date for Passover.) Check on a search engine if the dates you determined for Easter Sunday and Passover for 1951 and 2015 are correct.
3B- There is an accidental astronomical relationship between the two main calendars in use today, the solar calendar and the lunar calendar.
The calendar is based on three key astronomical events.â—¾ * A day, which is the time from one sunrise to the next sunrise - one complete rotation of the Earth. * A calendar year, which is approximately 365.2425 days - one complete orbit of Earth around the Sun. * A lunar month, which is approximately 29.53059 days - one complete orbit of the Moon around the Earth.
Multiply 19 solar calendar years by the number of days in a year. (Multiply 19 x 365.2425). Show that the number you obtain is almost exactly equals the same total number of days in 235 lunar months. (Multiply 235 x 29.53058).
3C- From the moon sites above, find the status (shape) of the moon on your birthdate in 2017. Also find the shape of the moon on your birthdate 19 years earlier (in 1998). What was the shape of the moon on each of those dates and why are the two very closely the same?
Explanation / Answer
The population of a large city like New York City is about 4£106 people. There are about 1:54 people per household. Ap-proximately 1 household in 19:5 has a piano.
The piano keyboard has about 64 notes (8 octaves) with about 2 strings per note. A piano should be tuned once per year (365.25 days).A piano tuner can tune about 4 pianos perday. And, finally, piano tuners work 252 days per year.
2)
Actual time = observer's time x
where is the relativistic time contraction factor.
= 1/(1–V²/c²)
speed = distance / Actual time = distance / observer's time x
speed = V = 4.3 LY / (3.8Y x )
but since we are using distance in LY and time in Y, speed is LY/Y, or actually V/c
V/c = 1.1316 (1/) = 1.1316(1–V²/c²)
V²/c² = 1.2805(1–V²/c²)
V²/c² = 1.2805–(1.2805)(V²/c²)
(2.2805)V²/c² = 1.2805
V²/c² = 0.5615
V/c = 0.7493
or 75% of light speed or 2.246e8 m/s
check
= 1/(1–V²/c²) = 1/(1–0.5615) = 1.510
At that speed it takes (outside observer) 4.3/0.75 = 5.73 years to make the trip.
relativistic contraction changes that, for the traveler, to 5.73/1.51 = 3.80 years
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