re Activity: A Walk in the Desert (1 and 2)

diamond777 · 2011-08-21 20:16:52

I have worked hard on both of the above and having completed "1" - the distance one and being well advanced with "2" - the angle/bearing one ..........
would someone please tell me if i am on the right track.
May i point out that there appears to be a difference between the figure shown for distance walked altogether up to point C
in part "1" this is shown as 6 (kilometers)
whereas in part "2" the same figure is shown as 4 (kilometers)

I have proceeded using the figure from part "1" - namely 6 kms.

My calculated figures for the three figure bearings for points C, D, and E are respectively 348.7, 264.3 and 265.9 (all degrees of course)

Please advise if these figures of mine are correct. If they are I will proceed to attempt to calculate the similar figures for points F G H I and J which are calculated using polar coordinates rather than the cartesian coordinates used for points A to E.

My thanks in anticipation...........
diamond777

bobbym · 2011-08-21 21:17:48

Hi diamond777;

Could you please post the link?

Bob · 2011-08-21 22:54:56

hi bobbym

I expect the links are

http://www.mathsisfun.com/activity/walk-in-desert.html

and

http://www.mathsisfun.com/activity/walk … ert-2.html

Bob

Last edited by Bob (2011-08-21 22:55:43)

Bob · 2011-08-21 23:34:24

hi diamond777

My calculated figures for the three figure bearings for points C, D, and E are respectively 348.7, 264.3 and 265.9 (all degrees of course)

Sorry, but I don't get any of these.

At point C, Jade has gone 2 East and 1 - 3 North or 2 South.

So taking O as the origin (0,0) the coords for C are ( 2,-2). To get back to the aircraft is a bearing of 315.

Because of the way the points are distributed around O you will always get an answer above 270, then one under 90, then one in the range 90 to 180, and then between 180 and 270; before following this sequence again.

How did you get 348.7? Maybe I can work out what's going on.

Bob

Last edited by Bob (2011-08-21 23:54:14)

diamond777 · 2011-08-22 03:37:22

hallo Bob
thanks for your response
I think I have done too much without the assurance that what i have done to date is correct.
I will give below the figures that i have arrived at for the distances (part one) to begin with as i would like to get that right before i go on to the directions (bearings) which if calculated from wrong distance information are just wasted time and effort, something i feel frustrated about at present.
so from part one my distance figures.
these of course are calculated as per the right angled triangle method as shown in part one.
point distance walked altogether distance in a straight line from O
O 0 0
A 1 1
B 3 sq rt of 5
C 6 (shown as 4 in part two) i have used 6) sq rt of 8
D 10 sq rt of 8
E 15 " " " 13 (this one agrees with an example given in part one)
F 21 " " " 25
G 28 " " " 32
H 36 " " " 32
I 45 " " " 41
J 55 " " " 61
though i have gone further than this i would like to get this (part one) correct in my mind before proceeding further again.
hope you understand my reluctance to spend too much time without some degree of assurance that i am on the right track (or not as the case may be.)
sincerely
David (diamond777)

Bob · 2011-08-22 04:46:57

hi David,

All those figures are the same as mine. (6 is right for C; the 4 is just a typo)

I also worked out the co-ordinates for each point. Then I used 'arctan' to calculate angles.

But bearings are always given clockwise from North, so I found I needed to do a little work to get the bearings from the angles I'd found.

Have a look at the diagram with my previous post. The points circle around the origin with every fourth point back in the same quadrant.

Also check you are doing the angles correctly. I used an Excel spreadsheet. Excel has a commend 'atan' which gives angles in radians, not degrees, so I had to convert using x180/pi.

Calculators will usually work with degrees or radians but you need to check which has ben set.

Bob

Last edited by Bob (2011-08-22 04:48:12)

diamond777 · 2011-08-22 07:16:14

Hi again Bob
Now that I have digested at least some of what you have told me, I have been able to clear up somewhat and can now turn my attention to what remains to be clarified in my mind.

The part one figures of mine seem to be ok. I did proceed on the assumption that the point C figure of four was a typo.

I am trying to follow the text itself (of the activity) and the given examples, figures and methods described.
Also noting relevant information such as how to calculate the three figure bearings and the fact that the text indicates to only use polar coordinates for points F to J. (and to use right angled triangles such as the one in the text labelled "OAB" for the points up to E only - this is how i attempted to arrive at three figure bearing figures (non-polar) for points up to and including point E.)

Perhaps this time around you could check my coordinates copied from the text as:

X Y Point
0, 0 O
0, 1 A
2, 1 B
2, -2 C
-2, -2 D
-2, 3 E
4, 3 F
4, -4 G
-4, -4 H
-4, 5 I
6, 5 J

Meanwhile i will try again with the three figure bearing figures back to O from points C, D and E. I note that
your figure for C was 315 degrees. Also what you wrote about the sequence.

From the square root figures for distances back to zero I calculate the following kilometer figures back to zero from:
point B 2.24 km point C 2.83 km point D as point C 2.83 km point E 3.61 km point F 5.00 point G and point H 5.66 km point I 6.40 km and, finally, point J 7.81 km. Do these figures look right to you?

many thanks for "bearing" with me. (no pun intended...)

Bob · 2011-08-22 07:24:32

hi David,

Yes. I agree with all of those.

Bob

diamond777 · 2011-08-22 18:16:48

Hi Bob
just after 7 am here in uk
a quick question
re the five column table in part two
column two (from the left) is headed "value of r" - r being one of the polar coordinates
it seems pretty obvious but i need to be certain .....are all the true figures for this column as the ones in the table from part one headed "distance (in a straight line) from O"?
david

Bob · 2011-08-22 20:55:36

hi diamond777,

I'm in the UK too. You got up earlier than me!

The 'r' in polar coordinates is the distance from the origin to the point, so, yes, they're the same thing.

On my spreadsheet for this, I made the following columns:

point expressed as a letter
number of the point with O = zero, A = 1 etc *
x coordinate of the point **
y coordinate of the point **
distance along the route *
straight line distance from O ( = r ) **
bearing. **

I tried to make everything using formulas, so that I could just copy and paste.

So distance along the route is found using a formula from number of the point

straight line distance and bearing are calculated from the two coordinates.

Because of the '4 quantrant effect' I needed to establish the first 4 lines of formulas before copy and paste would work.

Bob

diamond777 · 2011-08-22 21:27:35

thanks for that bob
i live in Stafford - the county town
my next step will be to calculate the column for value of the angle (can't find the proper sign on the keyboard) - but only down to point E - using the right angled triangle method shown in the part two text.
At the moment i am unsure of how to do this - despite having done all of the triangle stuff on maths is fun.
till next time .............
david

Bob · 2011-08-22 23:50:53

hi diamond777

I've made a diagram for those points only. The atan(y/x) function gives the angles as shown. So you then need to add or subtract 90 or 180 or 270 to get the correct bearing. The diagram should make it clear what you need to do in each case.

Bob

MathsIsFun · 2011-08-22 23:55:30

I didn't create those two activities (Les Bill Gates did), but I would love to hear feedback / ideas for improvement so we can make them better for future users.

Bob · 2011-08-22 23:59:34

hi MIF

There's a typo on WITD 2. the distance walked for C should be 6. It's correct on WITD 1

I like it as it is. It's a good way to introduce / use pythag, bearings and tan.

Bob

MathsIsFun · 2011-08-23 09:32:28

OK, will fix

diamond777 · 2011-08-23 23:05:19

hi Bob
thanks for your latest - I have made my own copy

what i really need to do now is to calculate the bearing for point C using the right angled triangle method.
I believe your figure was 315 degrees which seems to indicate that with my chosen method 315 would be arrived at from 360 - 45 degrees = 315 degrees?

But if that is so - i cannot see from the calculation given in the text for point B
(1/2 = 0.5 atan (0.5) = 26.6 degrees) how i do the equivalent calculation for point C
That is my current sticking point (there i go again with my unintended puns)

My current thinking is that i would like to calculate three figure bearings for all of the points using cartesian coordinates and then convert them all to polar coordinates in the way that the text describes.

Am i right in thinking that "cartesian" is effectively the same as "rectangular" (as opposed to polar) in the context of coordinates? What i mean to say is rectangular in the sense of being calculated using right angled triangles.
I hope i am making sense and transferring my thoughts effectively.
This could run and run as they say ...............
David

Bob · 2011-08-23 23:41:49

hi David

Not run and run. This is a walk in the desert. So take your time. I'll get you there.

To get the bearings, you've got to picture standing at the point (A,B C or whatever) and looking back towards O. A compass will tell you which way is North at that point and then you can calculate the bearing and walk back along it.

A: It's straight down to O; so bearing = 180

B: atan(0.5) = 26.6, but Jade has got to go back to O on a bearing.

Clockwise from North to West is 270. But that's too far, so I did 270 - 26.6 = 243.4. (see diagram)

C: atan(2/2) = 45.

If Jade is at C, the bearing of West from there is 270, add another 45 and you're pointing at O = 270 + 45 = 315.

D: atan(2/2) = 45 again.

But this time Jade has got to go North East = bearing 045 to get back to O.

E: atan(3/2) = 56.3

But if Jade is at E, then a bearing of 90 will mean go East from there. that's not enough. We want another 56.3 making 146.3.

And so on.

Bob

ps. Cartesian coordinates comes from the 'inventer', Rene Decartes.

He had an x axis across and a y axis up the page. As these are at right angles the grid looks like lots of rectangles so some people call these rectangular coordinates.

Polar coordinates are just another way of specifying a point in 2 dimensions.

I'll just mention (but don't let it worry you) that mathematicians have also devised coordinates systems where the axes aren't at right angles, and three dimensional versions. eeekkk!

Last edited by Bob (2011-08-24 00:01:15)

diamond777 · 2011-08-24 01:15:56

thank you Bob
that one is a break through

I recently saw a tv series by a prof. marcus de sautay (what a name) prof. of maths at i think oxford uni. I found the series very interesting and there i heard about Rene Descartes and others.

So
am i right in arriving at 225 degrees as the bearing from point D (270 - 45) ?

I think i will now play with my calculator and see if i can get it to give me the polar coordinates for points F - J inclusive. When i have the results i will "walk" them past you .......

All of this is keeping me occupied..........
till next time
David

diamond777 · 2011-08-24 02:04:50

hi bob
well i followed the instruction book for my calculator to program it for polar coords.
it finished with r=2,bearing=45 and this was displayed on the screen.
i was very unsure of what to do next - i had the feeling that another key or perhaps two were needed to , as it were, finish the process, but nothing else was indicated in the book.
so
i have, instead of proceeding with that, calculated the "rectangular coords for points F-J. that is to say the first part before the subtraction or addition to arrive at the three figure bearing.
below are my "first part figures:
from point F atan 3/4 (0.75) = 36.8 degrees
" " G " 4/4 (1) = 45 "
" " H " 4/4 (1) = 45 "
" " I " 5/4 (1.25)= 51.3 "
" " J " 5/6 (0.83)=39.7 "
If these figures are correct i will next do the conversion calculations to convert these to polar coords. (I will get back to doing the polar calcs on the casio .......)
I need a cup of tea now ...........
david

Bob · 2011-08-24 03:03:56

hi diamond777

The angles are ok but not always the conversion to bearings.

If you were at D and wanted to get back to O, you wouldn't get there by going on a bearing of 225. Look at diagram 1 below. You told me the bearing of D from O (ie. if you were at O, what way to get to D). So it's back to front.

And for F that's in roughly the same direction as B, so we need 2 hundred and something. You are still not seeing it from the point of view of where Jade is.

Jade wants to get back to the aircraft to get more supplies.

All you need to do is draw a diagram like mine, but picture Jade at the point and ask what way back to O.

I'll check again later this evening.

Bob

ps. With polar coordinates the angle is measured anticlockwise from the + x direction, so the polar coords will be different from the bearings. Let's make sure of the bearings first.

Last edited by Bob (2011-08-24 03:29:02)

diamond777 · 2011-08-24 05:51:59

hi bob
i am trying to do what you suggest but, so far i can only see:
D back to the start at O is up and right from quadrant 3 to point O
so D is in Q3 -x and -y territory
the text of part two says to subtract the angle from 270 degrees for certain points including point D (i think that this does not necessarily apply when following your advice)

point F is in Q1 F-O direction is down and left

Now i will try to focus on how to arrive at the bearing from the angle, taking into account all that you have said and what i am re-reading from the activity text.

watch this space .............
david

diamond777 · 2011-08-24 06:14:07

bob
i have not cracked it -
this is just a hunch/feeling but from what you have said recently i have deduced that the bearing from D to O may be 045 degrees
and that
the bearing from F to O may be 233.2 degrees?
are these bearings, at least, correct?

Bob · 2011-08-24 06:15:09

hi diamond777

stay on-line I'm composing a reply!

Bob

Bob · 2011-08-24 06:18:48

hi again,

What you have to do to the angle in order to get the bearing depends on which quadrant you are in.

270 - angle only works in quadrant 3, B, F, J, .....

You are right about D. It is 045

And F is 233.1

You getting there!

Bob

diamond777 · 2011-08-24 07:05:54

noted bob
i think i am aware of most of what the text says such as about which quadrant applies but there is something or there are some implications of some of the things in the text of which i am unaware (not blissfully i might add!)

Well i will come back to it tomorrow
david

Math Is Fun Forum

#1 2011-08-21 20:16:52

re Activity: A Walk in the Desert (1 and 2)

#2 2011-08-21 21:17:48

Re: re Activity: A Walk in the Desert (1 and 2)

#3 2011-08-21 22:54:56

Re: re Activity: A Walk in the Desert (1 and 2)

#4 2011-08-21 23:34:24

Re: re Activity: A Walk in the Desert (1 and 2)

#5 2011-08-22 03:37:22

Re: re Activity: A Walk in the Desert (1 and 2)

#6 2011-08-22 04:46:57

Re: re Activity: A Walk in the Desert (1 and 2)

#7 2011-08-22 07:16:14

Re: re Activity: A Walk in the Desert (1 and 2)

#8 2011-08-22 07:24:32

Re: re Activity: A Walk in the Desert (1 and 2)

#9 2011-08-22 18:16:48

Re: re Activity: A Walk in the Desert (1 and 2)

#10 2011-08-22 20:55:36

Re: re Activity: A Walk in the Desert (1 and 2)

#11 2011-08-22 21:27:35

Re: re Activity: A Walk in the Desert (1 and 2)

#12 2011-08-22 23:50:53

Re: re Activity: A Walk in the Desert (1 and 2)

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Re: re Activity: A Walk in the Desert (1 and 2)

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Re: re Activity: A Walk in the Desert (1 and 2)

#15 2011-08-23 09:32:28

Re: re Activity: A Walk in the Desert (1 and 2)

#16 2011-08-23 23:05:19

Re: re Activity: A Walk in the Desert (1 and 2)

#17 2011-08-23 23:41:49

Re: re Activity: A Walk in the Desert (1 and 2)

#18 2011-08-24 01:15:56

Re: re Activity: A Walk in the Desert (1 and 2)

#19 2011-08-24 02:04:50

Re: re Activity: A Walk in the Desert (1 and 2)

#20 2011-08-24 03:03:56

Re: re Activity: A Walk in the Desert (1 and 2)

#21 2011-08-24 05:51:59

Re: re Activity: A Walk in the Desert (1 and 2)

#22 2011-08-24 06:14:07

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