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Portfolio Type II -- Running with Angie and Bonnie

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simply input it into geogebra? I'm not sure though since I'm not familiar with the software. why not use your calculator? I honestly think TI has a much nicer interface than geogebra and is a lot easier to use.

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Hi guys,

I've found the angles of Buddy's changes in direction, but how do I obtain a recursive formula from them? I see no apparent pattern...

The values(in degrees) I got for the angles are:

3.434

7.689

13.524

20.839

32.990

60.684

Please help! :)

Edit:

I figured out that the recursive formulae is determined simply by trig, but now I'm confused about the discrete mathematical model I'm supposed to establish from them...are discrete models just normal equations that you plug values into? or are they recursive as well?

Edited by procrastinator

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aaaand... what is the relationship between finding the coordinates and calculating the angles? are the angles the coordinates or what? i mean, we couldve find the coordinates by merely measuring right?

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i have the same portfolio and its due tomorrow :'(

i've tried doing the phytagoras theorem but then i realized there are limits in this question as well.. My teacher didn't give me any information at all, just the stupid sheet.

please helppp :'(

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hey i really do like the way you guy respect the ib objesctive.... i do too

i just happen to be really worried man, i gt to give in this thing by tomorrow morning

all i need is the method by which one can find the coordinates of buddy

wat i have gt is by using

tan inverse of theta

sin inverse of theta * hypotaneus (the distance travelled by buddy in t seconds)

cos inverse of theta * hypotaneus (the distance travelled by buddy in t seconds)

and guess wat i have gt a perfect parabolla but it does not see to tourch the y axis

it stops around 3/4th of the way

You're on the right track. Try putting Angie and Buddy's positions into a right triangle. Buddy will travel along the hypotaneus, so his x and y coordinates could be defined using the other two sides of the right triangle. Hint: use arctan. Also note Angie's distance traveled along the vertical axis and Buddy's coordinate on the horizontal axis => these are your other two sides of the triangle. To find the distance traveled simply use S=vt.

Hint: Your first theta angle found will be arctan(1/17). Try to figure out your recursive formula accordingly.

Oh and I don't think my orbit looks like a parabola :-/ if Buddy catches up with Angie that means the curve will HAVE to touch the y-axis at one point.

just wondered, did everyone get arctan(1/17) for the first angle? coz i somehow didnt, and i'm afraid it's either me or it depends on the data (speed/distance/time) :bawling:

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Hi, I'm really new at this stuff. But I DO NEED HELP!

Can anybody tell me what is it understood by discrete model

I'm desperate.. and I must have this for wednesday u_u

HL:

Biology

Math

English B

Spanish A1

SL:

Philosophy

Physics

Edited by Frigo Canapé

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Okay, so it asks to uses trig to find coordinates where Buddy changes his direction. However, I'm quite lost even at this point. If we use trig, which three sides do we use? And if we find angles, how does that help us find the actual coordinate? It'll just simply give us the angle change. :(

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Hi, I'm really new at this stuff. But I DO NEED HELP!

Can anybody tell me what is it understood by discrete model

I'm desperate.. and I must have this for wednesday u_u

HL:

Biology

Math

English B

Spanish A1

SL:

Philosophy

Physics

discrete means discontinuous. so instead of having a curve, you have dots/points and connecting lines.

and FYI, you can go to profile, edit profile, signature to put your subjects rather than writing it in every post. :)

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ok, so i got a parabola that goes throughtout buddys curve, but my teacher said it wad to be a log model? help please?

and also what assumptions? like assumptions do we have to talk about?

Probably a little late to answer your question but for anyone else, the assumptions you need to mention are all the factors that occur in real life that you model doesnt account for. What you assume Angie and Buddie will do and the environment they are in that probably wouldnt occur perfectly in reality like the model shows it for. For example, Angie and Buddy are not dots moving. There are many assumptions made and you need to mention and you want to be able to explain quite a few of these.

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Hey all.

I just started this portfolio and it's gone well so far. I'm a little confused on the recursive formulae part, however.

I have one for the x-coordinate, but my formula for the y-coordinate involves using the previous x-coordinate, i.e. X(n-1).

Is this acceptable, given that I'm finding the x-coordinate before the y-coordinate, or do my formulae have to be completely in terms of x and y respectively?

Thanks in advance! :)

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edit: Another quick question, "construct a diagram to plot the positions and directions of both runners. Use trigonometry to find the coordinates of several points where Buddy changes his direction"

Do I have to find all the coordinates until they meet? If so, what if Buddy gets in the water? Do I have to re-do it with different values for v and u or just continue?

This is key point in the Modelling portfolio, Trigonometry, just like I said in the comment before me. You need to do a route which is to scale in a graph paper and then you look at Buddy's (not Bonnie) positions and then you find the angle of it. You can find different angles depending in which you will use SOH CAH TOA < you know these right.

After using these for almost the first 5 or 6 positions, you will then notice a pattern there of angles. A decreasing pattern or an increasing patter as I said it depends to the SOH CAH TOA. But what I remember but not sure because Im away from my portfolio that I used the SOH and found a decreasing pattern.

Later on you will need to find the formula of the pattern as I said.

regarding Buddy going on water. There will be an intersection point in the y-axis and at that point I assumed that he will stop and will change his angle completely toward Angie and then the modelling finish. Then after that you will have to do with different scenarios meaning different values of distance, speed etc...

I hope its useful and understandable

i am pretty sure no one's gonna respond, but i've been staring at this thread forever and i'm still far from a solution.

MR.AHM, after you drew buddy's route, which is the hypotenuse of the little triangles, did you measure the other two sides of the triangle manually? so you only used trig to find the angle, but not the sides, am i right?

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edit: Another quick question, "construct a diagram to plot the positions and directions of both runners. Use trigonometry to find the coordinates of several points where Buddy changes his direction"

Do I have to find all the coordinates until they meet? If so, what if Buddy gets in the water? Do I have to re-do it with different values for v and u or just continue?

This is key point in the Modelling portfolio, Trigonometry, just like I said in the comment before me. You need to do a route which is to scale in a graph paper and then you look at Buddy's (not Bonnie) positions and then you find the angle of it. You can find different angles depending in which you will use SOH CAH TOA < you know these right.

After using these for almost the first 5 or 6 positions, you will then notice a pattern there of angles. A decreasing pattern or an increasing patter as I said it depends to the SOH CAH TOA. But what I remember but not sure because Im away from my portfolio that I used the SOH and found a decreasing pattern.

Later on you will need to find the formula of the pattern as I said.

regarding Buddy going on water. There will be an intersection point in the y-axis and at that point I assumed that he will stop and will change his angle completely toward Angie and then the modelling finish. Then after that you will have to do with different scenarios meaning different values of distance, speed etc...

I hope its useful and understandable

i am pretty sure no one's gonna respond, but i've been staring at this thread forever and i'm still far from a solution.

MR.AHM, after you drew buddy's route, which is the hypotenuse of the little triangles, did you measure the other two sides of the triangle manually? so you only used trig to find the angle, but not the sides, am i right?

I know the question is not to me, but what I did is drew it manually to scale on a piece of graph paper and found the angles of Buddy each time he looks up. Then used trig to find the change in the y-axis ( upward) and the change in the x-axis (to the right)

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i am pretty sure no one's gonna respond, but i've been staring at this thread forever and i'm still far from a solution.

MR.AHM, after you drew buddy's route, which is the hypotenuse of the little triangles, did you measure the other two sides of the triangle manually? so you only used trig to find the angle, but not the sides, am i right?

The hypotenuse of each little triangle represents Buddy's speed, right?

The legs represent Angie's vertical distance and Buddy's distance from the y-axis respectively.

Using these two pieces of information, and knowing that the triangle represents both distance and speed, you can find the angle and components of Buddy's speed using trigonometry, as the investigation asks you to.

I had a quick question too. I have written a paragraph about the model's assumptions, one about it's mathematical limitations (i.e. some stuff I had to manually do that the formulae I came up with didn't account for), and am trying to write one about its limitations when applied to other situations. What does IB mean by "other situations"? Is it just other velocities, time intervals, distances, or other kinds of runners, or what?

Any help is appreciated, thanks.

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edit: Another quick question, "construct a diagram to plot the positions and directions of both runners. Use trigonometry to find the coordinates of several points where Buddy changes his direction"

Do I have to find all the coordinates until they meet? If so, what if Buddy gets in the water? Do I have to re-do it with different values for v and u or just continue?

This is key point in the Modelling portfolio, Trigonometry, just like I said in the comment before me. You need to do a route which is to scale in a graph paper and then you look at Buddy's (not Bonnie) positions and then you find the angle of it. You can find different angles depending in which you will use SOH CAH TOA < you know these right.

After using these for almost the first 5 or 6 positions, you will then notice a pattern there of angles. A decreasing pattern or an increasing patter as I said it depends to the SOH CAH TOA. But what I remember but not sure because Im away from my portfolio that I used the SOH and found a decreasing pattern.

Later on you will need to find the formula of the pattern as I said.

regarding Buddy going on water. There will be an intersection point in the y-axis and at that point I assumed that he will stop and will change his angle completely toward Angie and then the modelling finish. Then after that you will have to do with different scenarios meaning different values of distance, speed etc...

I hope its useful and understandable

i am pretty sure no one's gonna respond, but i've been staring at this thread forever and i'm still far from a solution.

MR.AHM, after you drew buddy's route, which is the hypotenuse of the little triangles, did you measure the other two sides of the triangle manually? so you only used trig to find the angle, but not the sides, am i right?

I know the question is not to me, but what I did is drew it manually to scale on a piece of graph paper and found the angles of Buddy each time he looks up. Then used trig to find the change in the y-axis ( upward) and the change in the x-axis (to the right)

OHH THANK YOU FOR REPLYING!! :)

well, i have drawn the routes on scale...and made little triangles... how did you find the angles? using trig as well? because if I find the angles using trig (by measuring the lengths of the vertical or horizontal component of the little triangles), i got angles with no particular pattern. If i manually measure the angles using a protractor, I am finding a pattern. so should I better use a protractor? :S

i am pretty sure no one's gonna respond, but i've been staring at this thread forever and i'm still far from a solution.

MR.AHM, after you drew buddy's route, which is the hypotenuse of the little triangles, did you measure the other two sides of the triangle manually? so you only used trig to find the angle, but not the sides, am i right?

The hypotenuse of each little triangle represents Buddy's speed, right?

The legs represent Angie's vertical distance and Buddy's distance from the y-axis respectively.

Using these two pieces of information, and knowing that the triangle represents both distance and speed, you can find the angle and components of Buddy's speed using trigonometry, as the investigation asks you to.

I had a quick question too. I have written a paragraph about the model's assumptions, one about it's mathematical limitations (i.e. some stuff I had to manually do that the formulae I came up with didn't account for), and am trying to write one about its limitations when applied to other situations. What does IB mean by "other situations"? Is it just other velocities, time intervals, distances, or other kinds of runners, or what?

Any help is appreciated, thanks.

does the hypotenuse not mean the distance travelled by buddy during the time interval? so hypotenuse -> s=vt? so not the speed?

and how do you now buddy's distance from the y-axis (besides measuring manually)?

PLEASE HELP ><

i actually have ideas regarding the "other situations". maybe it asks us to evaluate that the environment, in which buddy and angie are running... maybe the ground isn't always smooth so that buddy (and angie) wouldnt always run at constant speed...? or probably that buddy didnt have a timer to know when to look up...? just random thoughts :D

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does the hypotenuse not mean the distance travelled by buddy during the time interval? so hypotenuse -> s=vt? so not the speed?

and how do you now buddy's distance from the y-axis (besides measuring manually)?

PLEASE HELP ><

i actually have ideas regarding the "other situations". maybe it asks us to evaluate that the environment, in which buddy and angie are running... maybe the ground isn't always smooth so that buddy (and angie) wouldnt always run at constant speed...? or probably that buddy didnt have a timer to know when to look up...? just random thoughts :D

Well, actually, the hypotenuse represents both, but you don't need to know that distance to solve for the angle, just use the legs. Then you can use the hypotenuse representing his total speed and the angle to find the components and find out how far he travels in each time interval.

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