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gordonm888
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gordonm888
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December 18th, 2020 at 10:54:41 AM permalink
I've been off the forums for a few days and missed some juicy puzzles.

I am a physicist, so let me say that neglecting air resistance is a much bigger factor in a rocket's trajectory than the other factors mentioned. But yes, change of gravity with distance to the center of the earth will have a tiny effect on trajectory as will change of air density with elevation.

In fact it might be fun to repeat the puzzle, adding in the air resistance for a single cone shape and do the calculation for sea level and for the top of Mt Everest (or Denver) taking into account the altered air density and tiny changes in gravity.

P.S.,Two notes:
1. the coriolis effect will change the latitude of the rocket's landing point, but I don't think it is a primary factor that changes the time of flight, assuming the elevation of the earth's surface is unchanged at its altered landing point. Although, the rotational velocity of the earth's atmosphere does change with elevation which might introduce some lateral air drag as the rocket rises which would reduce its overall kinetic energy (!)

2. I think that change in mass due to the burning of fuel is not an issue if the firework is based on an explosion at the launch point, because then the fuel is oxidized and ejected almost instantaneously. However, fireworks usually have two packets of explosive material -one to launch it upwards and a second that is timed to explode at the top of its flight, creating the fireworks effect. The second explosion not only eliminates the mass of the fuel (and part of the rocket itself) but serves as an accelerant for the fragments of the rocket. For the purpose of posing a problem, it is probably best to assume the firework rocket does not explode in flight, LOL.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Wizard
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Wizard
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December 19th, 2020 at 6:27:44 AM permalink
I figured air resistance and gravity were factored into the problem with the acceleration factors given.

I'm not trying to be a Christmas Grinch. I'd be interested to see how these factors change at various altitudes and latitudes. As I recall, acceleration due to gravity ranges from about 9.6 to 10, depending on latitude, higher closer to the equator.
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Gialmere
Gialmere
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December 21st, 2020 at 8:32:34 AM permalink
A merry Monday! Time for music...



Many Christmas songs have lyrics in which a word or phrase is repeated. Several repetitive lyrics have been extracted from a number of holiday favorites.

Each algebraic expression below represents a song, where each word is represented by its first letter and exponents show the number of repetitions. If two or more words are repeated as a group, they appear in parentheses. For example, (JB)^2 is short for "Jingle Bells, Jingle Bells."

Can you identify all the songs below?
1. (JB)^3R
2. P(RP^3)^3
3. FL^8
4. (SIHP)^2
5. N^4
6. (WWYAMC)^3
7. (OCT)^2
8. OTO(CAJ)^2OTOCAJ
9. (GIED)^2
10. (OCLUAH)^2
11. (H^3WWG)^2
12. (LIS)^3
13. (FN)^3
14. (SB)^2
15. (HCSC)^2
16. (RTSJ)^2 R^2TSJ
17. (OC)^2E
Have you tried 22 tonight? I said 22.
ThatDonGuy
ThatDonGuy
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Thanks for this post from:
Gialmere
December 21st, 2020 at 10:25:15 AM permalink

1. Jingle Bell Rock (Jingle Bell, Jingle Bell, Jingle Bell Rock)
2. The Little Drummer Boy (Puh Rum-Pum-Pum-Pum, Rum-Pum-Pum-Pum, Rum-Pum-Pum-Pum)
3. Deck the Halls (Fa La La La La, La La La La)
4. Silent Night (Sleep In Heavenly Peace, twice)
5. The First Noel (Noel, Noel, Noel, Noel)
6. We Wish You A Merry Christmas (title, three times)
7. O Christmas Tree (title, twice)

9. Angels We Have Heard On High (Gloria, In Excelsis Deo)
10. O Come All Ye Faithful (O Come Let Us Adore Him, twice)

12. Let It Snow, Let It Snow, Let It Snow (title)

14. Silver Bells (title, twice)
15. Here Comes Santa Claus (title, twice)

17. O Come, O Come Emmanuel (title)

Last edited by: ThatDonGuy on Dec 21, 2020
chevy
chevy
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Gialmere
December 21st, 2020 at 10:38:11 AM permalink
I can add


2. Little Drummer Boy (pa rum pum pum pum)

11. Up on the housetop (ho, ho, ho, who wouldn't go)
13. Feliz Navidad
14. Silver Bells

Joeman
Joeman
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Gialmere
December 21st, 2020 at 10:48:57 AM permalink

1. Jingle Bell Rock
2. Little Drummer Boy ?
3. Deck The Halls
4. ???
5. The First Noel
6. We Wish You a Merry Christmas
7. O Christmas Tree
8. God Rest Ye Merry Gentlemen
9. ???
10. O Come All Ye Faithful
11. Up on the Houestop
12. Let It Snow!
13. ???
14. Silver Bells
15. Here Comes Santa Claus
16. Joy to the World!
17. ???
"Dealer has 'rock'... Pay 'paper!'"
ssho88
ssho88
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December 21st, 2020 at 4:51:53 PM permalink
Quote: gordonm888


1. the coriolis effect will change the latitude of the rocket's landing point, but I don't think it is a primary factor that changes the time of flight, assuming the elevation of the earth's surface is unchanged at its altered landing point. Although, the rotational velocity of the earth's atmosphere does change with elevation which might introduce some lateral air drag as the rocket rises which would reduce its overall kinetic energy (!)



Regarding the coriolis effect, I am actually more interested in the initial HORIZONTAL speed of rocket.

Just before lunching, the horizontal speed of rocket at equator is about 460m/s due to the earth rotation, and just after lunching, there are two component, VERTICAL and HORIZONTAL speed, so the rocket actually move "slanting" from its vertical axis. Therefore, the rocket should travel a longer distance before reaching the target point and it take longer time. Am I missing something ? Hope can learn something from you.
Last edited by: ssho88 on Dec 21, 2020
Gialmere
Gialmere
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December 21st, 2020 at 8:25:07 PM permalink
Quote: ThatDonGuy


1. Jingle Bell Rock (Jingle Bell, Jingle Bell, Jingle Bell Rock)
2. The Little Drummer Boy (Puh Rum-Pum-Pum-Pum, Rum-Pum-Pum-Pum, Rum-Pum-Pum-Pum)
3. Deck the Halls (Fa La La La La, La La La La)
4. Silent Night (Sleep In Heavenly Peace, twice)
5. The First Noel (Noel, Noel, Noel, Noel)
6. We Wish You A Merry Christmas (title, three times)
7. O Christmas Tree (title, twice)

9. Angels We Have Heard On High (Gloria, In Excelsis Deo)
10. O Come All Ye Faithful (O Come Let Us Adore Him, twice)

12. Let It Snow, Let It Snow, Let It Snow (title)

14. Silver Bells (title, twice)
15. Here Comes Santa Claus (title, twice)

17. O Come, O Come Emmanuel (title)


Quote: chevy

I can add



2. Little Drummer Boy (pa rum pum pum pum)

11. Up on the housetop (ho, ho, ho, who wouldn't go)
13. Feliz Navidad
14. Silver Bells


Quote: Joeman


1. Jingle Bell Rock
2. Little Drummer Boy ?
3. Deck The Halls
4. ???
5. The First Noel
6. We Wish You a Merry Christmas
7. O Christmas Tree
8. God Rest Ye Merry Gentlemen
9. ???
10. O Come All Ye Faithful
11. Up on the Houestop
12. Let It Snow!
13. ???
14. Silver Bells
15. Here Comes Santa Claus
16. Joy to the World!
17. ???


Correct!

In a joint solve.



1. "Jingle Bell Rock" ("Jingle Bell, Jingle Bell, Jingle Bell Rock")
2. "The Little Drummer Boy" ("Pa Rum Pum Pum Pum, Rum Pum Pum Pum, Rum Pum Pum Pum")
3. "Deck the Halls" ("Fa La La La La La La La La")
4. "Silent Night" ("Sleep in Heavenly Peace, Sleep in Heavenly Peace")
5. "The First Noel" ("Noel, Noel, Noel, Noel")
6. "We Wish You A Merry Christmas" ("We Wish You A Merry Christmas, We Wish You A Merry Christmas, We Wish You A Merry Christmas")
7. "O Christmas Tree" ("O Christmas Tree, O Christmas Tree")
8. "God Rest Ye Merry Gentlemen" ("O Tidings Of Comfort And Joy, Comfort And Joy, O Tidings Of Comfort And Joy")
9. "Angels We Have Heard On High" ("Gloria in Excelsis Deo, Gloria in Excelsis Deo")
10. "O Come, All Ye Faithful" ("O Come, Let Us Adore Him, O Come, Let Us Adore Him")
11. "Up On The Housrtop" ("Ho, Ho, Ho, Who Wouldn't Go? Ho, Ho, Ho, Who Wouldn't Go?")
12. "Let It Snow" ("Let It Snow, Let It Snow, Let It Snow")
13. "Feliz Navidad" ("Feliz Navidad, Feliz Navidad, Feliz Navidad")
14. "Silver Bells" ("Silver Bells, Silver Bells")
15. "Here Comes Santa Claus" ("Here Comes Santa Claus, Here Comes Santa Claus")
16. "Joy To The World" ("Repeat The Sounding Joy, Repeat The Sounding Joy, Repeat, Repeat The Sounding Joy") [A toughie since it uses lyrics from verse 2]
17. "O Come, O Come Emmanuel" ("O Come, O Come Emmanuel")

--------------------------------------


I'm giving up drinking till Christmas.

Bad punctuation, can't edit title

I'm giving up. Drinking till Christmas.
Have you tried 22 tonight? I said 22.
chevy
chevy
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December 21st, 2020 at 8:52:56 PM permalink
Is it still Monday? Is "Easy Monday" copyrighted, trademarked, patented or otherwise intellectually protected by Gialmere?

Problem 2 : (10 pts)

A circle of radius, r, is centered at the origin. An equilateral triangle with side, a, is also centered at the origin. Given the portion of the triangle outside the circle has the same area as the portion of the circle outside the triangle...

a: (7 pts) What is the side of the triangle, a, in terms of r ?
b: (3 pts) What is the total area of the three pointed portions of the triangle, in terms of r ? (i.e. portions outside the circle)


What did the triangle say to the circle?
ssho88
ssho88
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December 21st, 2020 at 9:42:13 PM permalink
Quote: chevy

Is it still Monday? Is "Easy Monday" copyrighted, trademarked, patented or otherwise intellectually protected by Gialmere?

Problem 2 : (10 pts)

A circle of radius, r, is centered at the origin. An equilateral triangle with side, a, is also centered at the origin. Given the portion of the triangle outside the circle has the same area as the portion of the circle outside the triangle...

a: (7 pts) What is the side of the triangle, a, in terms of r ?
b: (3 pts) What is the total area of the three pointed portions of the triangle, in terms of r ? (i.e. portions outside the circle)


What did the triangle say to the circle?





a) a = 2*(pi)^0.5/3^0.25 * r = 2.693547r
b) Total Area outside circle = 0.573249r^2




Triangle : why can't pi = 3 ?
Circle : LOL !
Last edited by: ssho88 on Dec 21, 2020

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