Math and scaling help?

[lizzy16]

Okay.

So heres the dealieo.

a. The sun has a diameter of 1,392,000 km

b. The Earth has a diameter of 12,756 km

c. The moon has a diameter of 3,476 km

d. A basketball has a diameter of 0.23 m= .00023 km

e. A km equals 1000

f. The distance from the center of the Earth to the center of the moon is: 384,403 km

g. The distance from the center of the Earth to the center of the sun: 149,600,000 km

The question is: 1. If the Earth was the size of a basketball, how big would the moon be?

And heres what i did:

.00023km /12,756km= .00000001803073064 KM

.00000001803073064X3476= .0000626748 KM

The moon would be . 0000626748 KM

Is this correct? :)

And, the next question is

2. If the Earth was the size of a basketball, how far away would the moon be? Note: You need to scale the distance not just the planets. If you change the diameter/radius of the planet, you also have to change the distance between them.

So, i know i need to get the .00023 km and figure out how the center would change from the object being smaller. How would i go about doing that?

[MarginOfError]

Okay.

So heres the dealieo.

The question is: 1. If the Earth was the size of a basketball, how big would the moon be?

And heres what i did:

.00023km /12,756km= .00000001803073064 KM

.00000001803073064X3476= .0000626748 KM

The moon would be . 0000626748 KM

Is this correct? :)

And, the next question is

So, i know i need to get the .00023 km and figure out how the center would change from the object being smaller. How would i go about doing that?

the ratio of the moon's diameter to the earth's is

3476/12756 = .272

So if the earth were the size of the basketball, the moon would be

.00023 * .272 = .00006256 km

for question 2,

384,403 * .272 = 104557.6 km

[lizzy16]

Wouldn't i need to change the 384, 403 since the .272 was changes?

[Dravin]

To double check your figures, if the following is true then the ratio between the bodies has been maintained Earth/Moon = Earth 2/Moon 2.

So, i know i need to get the .00023 km and figure out how the center would change from the object being smaller. How would i go about doing that?

The center of your bodies shouldn't be changing, only the radii. You may be over-thinking the question, couldn't you just apply the same factor you did to the bodies to the center to center distance? So if you had:

Body A = 50

Body B = 40

Distance center AB = 100

And you needed to scale them by a factor of 1/2, you'd get Body A = 25, Body B = 20, and Distance center AB = 50? If your problem isn't giving you center to center distance couldn't you just do Distance AB + Body A radius + Body B radius = Distance center AB and then work with that? To reverse the process to get a surface to surface distance from the new model just Scaled Distance center AB - Scaled Body A radius - Scaled Body B radius*. Though maybe I'm thinking too simply.

*Edit: It occurs to me that this may be unnecessary. At least in my example the surface to surface distance is 10, which turns into 5 when scaled. Which is the same answer the more convoluted approach gives (10/2 = (50-25-20).

Edited October 5, 2011 by Dravin

[Jennarator]

I shouldn't have read this thread,. I feel like an idiot.....

[Vort]

Okay.

So heres the dealieo.

a. The sun has a diameter of 1,392,000 km

b. The Earth has a diameter of 12,756 km

c. The moon has a diameter of 3,476 km

d. A basketball has a diameter of 0.23 m= .00023 km

e. A km equals 1000

f. The distance from the center of the Earth to the center of the moon is: 384,403 km

g. The distance from the center of the Earth to the center of the sun: 149,600,000 km

The question is: 1. If the Earth was the size of a basketball, how big would the moon be?

And heres what i did:

.00023km /12,756km= .00000001803073064 KM

.00000001803073064X3476= .0000626748 KM

The moon would be . 0000626748 KM

Is this correct? :)

Yes, you are right. Do you understand why, though? Or is it just "plug-and-chug"?

The key to doing problems like this is in making the comparison. "My son's size is to my size as the mountain's size is to X", then solve for X This is done by making ratios:

(My son's size)/(My size) = (The mountain's size)/(X)

Now it's easy to cross-multiply and solve for X:

X (My son's size) = (My size) (The mountain's size)/(My son's size)

X = (My size) (The mountain's size)

Same thing here. Instead of using whole phrases, let's define some variables to make things easy:

Earth diameter: E (= 12,756 km)

Basketball diameter: B (= 0.23 m, or 0.00023 km)

Moon's diameter: M (= 3,476 km)

So if the earth is a basketball, how big is the moon? In other words, E is to B as M is to X:

E/B = M/X

Solve for X:

XE = BM

X = BM / E

Now put in your values:

X = (0.23 m)(3,476 km) / (12,756 km) = 0.063 m, or 6.3 cm -- about 2.5 inches in diameter, roughly the size of a cue ball.

And, the next question is

So, i know i need to get the .00023 km and figure out how the center would change from the object being smaller. How would i go about doing that?

Sorry, don't understand what you mean. How would the center of what change from which object being smaller?

Edited October 5, 2011 by Vort

[sister_in_faith]

This thread reminds me of this funny 911 call...

A four year old calls 911 for help with 'take aways'... I've been watching a lot of police videos today, and this is what came to mind. It is so cute!

Math Homework 911 Call Sound Clip and Quote

best part is the end when the mom catches him:

Woman: Johnny what do you think you’re doing?!

Boy: The policeman is helping me with my math.

Woman: What did I tell you about going on the phone?

Operator: It’s the mother…

Boy: You said if I need help to call somebody.

Woman: I didn’t mean the police.

Edited October 5, 2011 by sister_in_faith

[lizzy16]

Yes, you are right. Do you understand why, though? Or is it just "plug-and-chug"?

X = (0.23 m)(3,476 km) / (12,756 km) = 0.063 m, or 6.3 cm -- about 2.5 inches in diameter, roughly the size of a cue ball.

The plug and chug. I won't need this ever again. This is for a stupid science class assignment. I'll never be doing it again.Ever.

And, i don't think i can multiple .23m by 3476 km. The units are different..so that wouldn't work.

[Dravin]

The plug and chug. I won't need this ever again. This is for a stupid science class assignment. I'll never be doing it again.Ever.

And, i don't think i can multiple .23m by 3476 km. The units are different..so that wouldn't work.

If you know what 1ft + 6in equals then you understand how you can multiply 0.23m by 3476km.

[Vort]

The plug and chug. I won't need this ever again. This is for a stupid science class assignment. I'll never be doing it again.Ever.

You are mistaken, Lizzy. You will indeed need this again, throughout your life. Don't deceive yourself into believing that math is useless. Nothing could be further from the truth.

And, i don't think i can multiple .23m by 3476 km. The units are different..so that wouldn't work.

Good for you for noticing the units! So many of my physics students didn't even bother looking at the units, and it always messed them up. In this case, the units are meter-kilometers, or square meters times a thousand. Since you then divide by kilometers, you are again left with meters.

[pam]

I shouldn't have read this thread,. I feel like an idiot.....

Then I am in very good company my dear.

[lizzy16]

Got it on the units thing.

As for math, I don't see why i'll be comparing the size of a basketball to earth. It's just confusing. If it was like, my height vs my friends and if i was the size of a pencil i could do that. I'd just cross multiply with the whole pencil/me=x/friends.....at least thats how i'd do it.

What about this-

The speed of light = 186,000 miles/second or 670,000,000 miles/hour

Distance from the surface of the Earth to the surface of the moon = 230,000 miles

Distance from the Earth to the sun = 93,000,000 miles

Distance from one side of the solar system to the other = 5,600,000,000 miles

6. How long would it take for light to go from the moon to the Earth?

I did 230,000 miles*670,000,000 miles/hour=154100000000000 miles^2/hour

Is there a way to just get it down to just by the hour? not..miles^2/hour?

[Dravin]

So many of my physics students didn't even bother looking at the units

That explains why you held onto derivatives when filing things away into the ol' noggin.

[Dravin]

I did 230,000 miles*670,000,000 miles/hour=154100000000000 miles^2/hour

Is there a way to just get it down to just by the hour? not..miles^2/hour?

It looks like you have it set up as D*R=T. That is incorrect, it should be D/R = T. A useful tip is to remember "dirt", that is D=RT (or Distance = Rate*Time), since you want time you solve it for T (by dividing both sides by R).

So you'd have X mi/y mph = x/y hours

Edited October 5, 2011 by Dravin

[LittleWyvern]

What about this-

The speed of light = 186,000 miles/second or 670,000,000 miles/hour

Distance from the surface of the Earth to the surface of the moon = 230,000 miles

Distance from the Earth to the sun = 93,000,000 miles

Distance from one side of the solar system to the other = 5,600,000,000 miles

6. How long would it take for light to go from the moon to the Earth?

Generally:

Let d be the distance from the moon to the Earth, and let c be the speed of light. The units of d is miles, the units of c are miles/second. So:

d miles * 1 seconds / c miles = d / c seconds.

Get that so far? We used the inverse of c, so instead of c being miles/second we needed seconds/miles, so I used 1 / c. That flipped the units. This let the units cancel out, leaving us with seconds, which is what we wanted. Substitute the values of d and c in to get your answer in seconds.

Note that we could have also used c as miles/hour (a different value), but then our result would have been in hours instead of seconds.

[lizzy16]

Okay.

So using your advice and my stellar knowledge heres what i came up with...if somoene would like to tell me if its wrong and a hint or whatever on how to correct it let me know :)

Part 1

Using the information given, answer the following questions (NOTE: if you need help with this

assignment, please visit the Math Lab or the Tutoring Center at the Academic Learning Center in the McKay Library). YOU MUST SHOW YOUR WORK TO GET FULL CREDIT.

a. The sun has a diameter of 1,392,000 km

b. The Earth has a diameter of 12,756 km

c. The moon has a diameter of 3,476 km

d. A basketball has a diameter of 0.23 m= .00023 km

e. A km equals 1000

f. The distance from the center of the Earth to the center of the moon is: 384,403 km

g. The distance from the center of the Earth to the center of the sun: 149,600,000 km

If the Earth was the size of a basketball, how big would the moon be?

the ratio of the moon's diameter to the earth's is

3476/12756 = .272

So if the earth were the size of the basketball, the moon would be

the ratio of the moon's diameter to the earth's is

3476/12756 = .272

.00023 * .272 = .00006256 km

2. If the Earth was the size of a basketball, how far away would the moon be? Note: You need to scale the distance not just the planets. If you change the diameter/radius of the planet, you also have to change the distance between them.

384,403 *.272=104557.6 km.

3. If the sun was the size of a basketball, how big would the Earth be?

. The ratio of the suns diameter to the earth would be 1,392,000 km/12,756 km= 109.125 km

4. If the sun was the size of a basketball, how far away would the Earth be? Note: You need to scale the distance not just the planets. If you change the diameter/radius of

he planet, you also have to change the distance between them.

109.125 km*149,600,000 km=16325100000km.

Part 2 D/R = T

Using the information given, answer the following questions (again, show your work).

The speed of light = 186,000 miles/second or 670,000,000 miles/hour

Distance from the surface of the Earth to the surface of the moon = 230,000 miles

Distance from the Earth to the sun = 93,000,000 miles

Distance from one side of the solar system to the other = 5,600,000,000 miles

Using D/R = T

5. How many miles can light travel in one year?

24x365=8760 hours.

8760 hours*670,000,000 miles/hour= 5,869,200,000,000 miles

6. How long would it take for light to go from the moon to the Earth?

230,000 miles/670,000,000 mph=.00034328356821 hours.

7. How long does it take for light from the sun to reach the Earth?

93,000,000 miles / 670,000,000miles/hour= .1388059701 hours

8. How long does it take for light to travel from one side of the solar system to the other?

5,600,000,000 miles/670,000,000= 8.3582 hours

[RipplecutBuddha]

This thread is a perfect display of why I'm so very grateful that reincarnation is not real, and that I will never have to go through High School ever again.

[lizzy16]

I'm in college :) But yes, math is awful :)

[beefche]

Okay.

So using your advice and my stellar knowledge heres what i came up with...if somoene would like to tell me if its wrong and a hint or whatever on how to correct it let me know :)

Part 1

Using the information given, answer the following questions (NOTE: if you need help with this

assignment, please visit the Math Lab or the Tutoring Center at the Academic Learning Center in the McKay Library). YOU MUST SHOW YOUR WORK TO GET FULL CREDIT.

Um, is it ok for you to post that here and ask for help? It specifically says to go to the Tutoring Center for help, not post it on the internet.

[lizzy16]

Um, is it ok for you to post that here and ask for help? It specifically says to go to the Tutoring Center for help, not post it on the internet.

Yea, its okay. The syllabus encourages us to work with others, form study groups ect. And, i did...until i realized they had less of a clue then I did. They did it a tottaly different way that I'm pretty dang sure was wrong. And, my roommates/neighbors aren't mathy people :) I've kind of exhausted my resources other then the tutoring center. My plan was to do the best I could, work it out the best I can and then go to the tutoring center tomorrow to double check my work. So yea, its fine. It's not as if i didn't try every problem on my own first.

[LittleWyvern]

Lizzy, a good way to check these kind of problems is to do it symbolically, or do it only with the units. If you start with the unit you are given, multiply by your conversions (the unit conversions, not the numbers, like miles/hour), and end up with the unit you wanted, then you most likely have the right answer. :)

[Captain_Curmudgeon]

The plug and chug. I won't need this ever again. This is for a stupid science class assignment. I'll never be doing it again.Ever.

This used to be called "The Rule of Three" or cross multiplication.

I use it about three or four times a week. It's how you scale recipes, figure out how much time and how much gas it will take you to get to Canada, etc.

They used to teach this in like the fourth grade.

[Dravin]

This used to be called "The Rule of Three" or cross multiplication.

I use it about three or four times a week. It's how you scale recipes, figure out how much time and how much gas it will take you to get to Canada, etc.

They used to teach this in like the fourth grade.

Interesting, I didn't know there was a particular rule to it. I always just solved my equations for the variable I need. Same result in the end but not as snazzy.

[Vort]

They used to teach this in like the fourth grade.

What a curmudgeonly thing to say. Wish I'd thought of it.

[lizzy16]

Lets close this thread :) I finished the assignment.