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iridemymuni
2006-11-05, 09:32 AM
hey, got an assignment due VERY soon should have done it earlier was too busy riding.

can anybody please help me work this out.

Task2:

The pilot of a small plane is attempting to land on a small airstrip, and the wheels hit the runway only 1000 metres short of a large group of trees at the end of the runway. The plane’s speed on the tarmac is modeled by the equation v = A-10^kt, where v the plane’s velocity in m/s, t is the time taken n seconds to come to a complete halt and A and K are constants.

*graph showing decelleration of plane*

If the pilot is attempting to land the plane at a speed of 80m/s,

a. Calculate the value of A (1 mark)
b. 8) investigate at least 3 different values of k between (but not including) 0.01 and 0.2 and for each value determine whether the plane comes to a complete stop before the end of the runway. Use any graphs and/or diagrams, any numerical techniques and any technology t
to support your arguments, justify your procedures. What physical conditions could make k vary? List assumptions you have made. Would there be any values of k (not just the values between 0.01 and 0.2) for which this equation could not be used to model the velocity of a plane landing on a tarmac? Give your reasons and justify your answer

ivan
2006-11-05, 09:47 AM
hey, got an assignment due VERY soon should have done it earlier was too busy riding.

can anybody please help me work this out.

Task2:

The pilot of a small plane is attempting to land on a small airstrip, and the wheels hit the runway only 1000 metres short of a large group of trees at the end of the runway. The plane’s speed on the tarmac is modeled by the equation v = A-10^kt, where v the plane’s velocity in m/s, t is the time taken n seconds to come to a complete halt and A and K are constants.

*graph showing decelleration of plane*

If the pilot is attempting to land the plane at a speed of 80m/s,

a. Calculate the value of A (1 mark)
b. 8) investigate at least 3 different values of k between (but not including) 0.01 and 0.2 and for each value determine whether the plane comes to a complete stop before the end of the runway. Use any graphs and/or diagrams, any numerical techniques and any technology t
to support your arguments, justify your procedures. What physical conditions could make k vary? List assumptions you have made. Would there be any values of k (not just the values between 0.01 and 0.2) for which this equation could not be used to model the velocity of a plane landing on a tarmac? Give your reasons and justify your answer

Okay, this is a bit confusing.

Just to verify, is it v = A - 10 to the power of (k times t) or is it v = A - (10 to the power of k) times t? The first one would be very strange and give a very unrealistic graph for deceleration. Is t 0 at touch-down? Could you post the exact wording from the text-book?

Edit: On a second thought, I'm not sure how realistic the graph would be. I guess it depends how the plane decelarates. If it's by reversing the turbines then it wouldn't be that bad, I guess.

iridemymuni
2006-11-05, 09:49 AM
thats the exact wording on the task sheet.

it is

v = a - (10 ^ kt)

i'm assuming t = 0 at touch down, yes.

Dave Coleman
2006-11-05, 09:51 AM
Okay, this is a bit confusing.

Just to verify, is it v = A - 10 to the power of (k times t) or is it v = A - (10 to the power of k) times t? The first one would be very strange and give a very unrealistic graph for deceleration. Is t 0 at touch-down? Could you post the exact wording from the text-book?

Edit: On a second thought, I'm not sure how realistic the graph would be. I guess it depends how the plane decelarates. If it's by reversing the turbines then it wouldn't be that bad, I guess.

You're a gun at maths, man.

ivan
2006-11-05, 09:56 AM
hey, got an assignment due VERY soon should have done it earlier was too busy riding.

can anybody please help me work this out.

Task2:

The pilot of a small plane is attempting to land on a small airstrip, and the wheels hit the runway only 1000 metres short of a large group of trees at the end of the runway. The plane’s speed on the tarmac is modeled by the equation v = A-10^kt, where v the plane’s velocity in m/s, t is the time taken n seconds to come to a complete halt and A and K are constants.

*graph showing decelleration of plane*

If the pilot is attempting to land the plane at a speed of 80m/s,

a. Calculate the value of A (1 mark)
b. 8) investigate at least 3 different values of k between (but not including) 0.01 and 0.2 and for each value determine whether the plane comes to a complete stop before the end of the runway. Use any graphs and/or diagrams, any numerical techniques and any technology t
to support your arguments, justify your procedures. What physical conditions could make k vary? List assumptions you have made. Would there be any values of k (not just the values between 0.01 and 0.2) for which this equation could not be used to model the velocity of a plane landing on a tarmac? Give your reasons and justify your answer


a) I think A will be 81 m/s. V should be 80m/s at touch-down(specified), so.
v = A - 10^kt => 80m/s + 10^(k*0) = 81m/s. This would really make much more sense(to me, at least) if it was something like t*10^k, but there we are.

iridemymuni
2006-11-05, 09:58 AM
yeah for the first part i too got 81 for A

p.s A isnt a speed, it's just a constant.
now im stuck at the second part

ivan
2006-11-05, 09:58 AM
You're a gun at maths, man.
Thanks, man.
You'll need to integrate to find if it will stop before the end of the runway or use the graphs somehow.

ps. Oh no, Naomi's reading this thread. Good, she'll correct me if I'm wrong.

ivan
2006-11-05, 10:00 AM
yeah for the first part i too got 81 for A

p.s A isnt a speed, it's just a constant.
now im stuck at the second part
Have you guys done integration? They wouldn't make you do something that you don't know how to do. What graphs do they give you?

iridemymuni
2006-11-05, 10:02 AM
yes they tought us about it.

no i dont remember any of it.

they ave us a graph that has time down the bonnom, which goes for 16 units, and no label on the y axis. there is a curse from the top left to the bottom right.

Muniacal
2006-11-05, 10:15 AM
Thanks, man.
You'll need to integrate to find if it will stop before the end of the runway or use the graphs somehow.

ps. Oh no, Naomi's reading this thread. Good, she'll correct me if I'm wrong.



I think you shuold get Mawsome to help solve the probelm. Ha ha.

Naomi
2006-11-05, 10:21 AM
. there is a curse from the top left to the bottom right.




A common attitude seen from a few of my students too. No respect for mathematics at all. :-)

Deserves to go into one of those lists of exam bloopers.


Nao

iridemymuni
2006-11-05, 10:31 AM
hahaha well spotted there naomi.


GOT A QUESTION

how do i use logs to figure out t

81 = 10 ^ 0.02t

if you can help, please do

Naomi
2006-11-05, 10:33 AM
yeah for the first part i too got 81 for A

p.s A isnt a speed, it's just a constant.
now im stuck at the second part

That's a good start, although A is not just a constant. Think about it.


Nao

iridemymuni
2006-11-05, 10:35 AM
it said it was a constant lol :s.

please help with the log thing. please please please

ivan
2006-11-05, 10:36 AM
hahaha well spotted there naomi.


GOT A QUESTION

how do i use logs to figure out t

81 = 10 ^ 0.02t

if you can help, please do

10^t=x
log(x)=t

So, log(81)/0.02=t

iridemymuni
2006-11-05, 10:39 AM
that gives me 95 seconds to stop.

if i investigate 2 other values of k i get"
k = 0.1
t = 19

19 seconds to stop

k = 0.19
t = 10

10 seconds to stop

am i on the right track here?

ivan
2006-11-05, 10:42 AM
Yes, I think so. Now you either have to have a graph for each value of k that you're testing and find the area under it by counting the squares(the old one) or integrate v=A - 10^kt and find the area between t=0 and t when v is 0. I'm still trying to figure out how to integrate the thing, can't think of a way.

iridemymuni
2006-11-05, 10:45 AM
hmmmm.

how do i graph for each value of k

i cant work it out

tomtrevor
2006-11-05, 10:46 AM
thats pretty much it, and thats pretty much what i got, except i used different values for k.

now you have to use the simpsons rule to find the area under it, like in task 1.

thats what i still have to do.

ivan
2006-11-05, 10:47 AM
Well, you could do it manually. Are you allowed calculators? Or you could also use the trapezium rule to find an estimate. I can't believe I didn't think of this before. That's probably the easiest solution in this situation.

iridemymuni
2006-11-05, 10:49 AM
i would use those rules but i dont know how to graph them !!

Naomi
2006-11-05, 10:49 AM
hahaha well spotted there naomi.


GOT A QUESTION

how do i use logs to figure out t

81 = 10 ^ 0.02t

if you can help, please do


OK a clue, although I will not do the assignment for you. ( Because I would be annoyed if my students used the same tactics. It is more important that I know they can't do it, than to know their uncle can. )

1000 =10 ^ 3

therefore: log 1000 (base 10) =3

and more generally

y =b ^ x

so log y ( base b) =x


OK?


Nao

tomtrevor
2006-11-05, 10:49 AM
i dont think we have to graph them

yea im gonna use the trap rule, much easier

ivan
2006-11-05, 10:55 AM
i would use those rules but i dont know how to graph them !!
You don't need to graph the trapezium rule. You have to make a table with two rows and many columns. In the upper column you have t in the lower you have v. Then, you put the smallest value of t(0) in the left row of the upper column and the largest value of t(depends on k) in the right row of the column. Then you divide the largest value of t by the number of values of t that you will be testing and increase t each time, putting it in the consecutive row.
Illustration from t = 0 to t = 4

t 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
v 80 75 68 an so on 0

Then, for each value of t find the value of v which it will give.
Then use the trapezium rule to find an estimate. I'll post it in a second(if you haven't found a better solution while I was typing this).

ivan
2006-11-05, 11:01 AM
OK a clue, although I will not do the assignment for you. ( Because I would be annoyed if my students used the same tactics. It is more important that I know they can't do it, than to know their uncle can. )
Nao

Are you a teacher, Naomi?

skianduniaddict
2006-11-05, 01:32 PM
i thpought i could help bt its a saturday and i cant to that porblem

iridemymuni
2006-11-05, 01:32 PM
haha

dont worry guys, i worked it out !!

THANKS

Naomi
2006-11-05, 06:40 PM
Are you a teacher, Naomi?


Well Sherlock...
I give a certain amount of university lecturies , mainly in physics, but also can at times get involved in some of the easier mathematics.

Nao

mornish
2006-11-05, 07:27 PM
this thread is so confusing to my simple mind:cool:

johnfoss
2006-11-06, 01:57 AM
Thanks to everyone who helped, without doing his homework for him. Great tutoring! Unfortunately it's all over my head so I would have been useless anyway.

On a second thought, I'm not sure how realistic the graph would be. I guess it depends how the plane decelarates. If it's by reversing the turbines then it wouldn't be that bad, I guess.
Based on the fact that it's a math (or maths) problem, I don't think the method of braking is relevant, nor does it have to be realistic as long as the math is right. At least the plane isn't landing on a conveyor belt... :)

tobbogonist
2006-11-06, 06:54 AM
i would love to be able to say: "you may all be very good at maths and blow me away with complicated sums, but when it comes to...."

But honestly i have no area of expertise that is even summountable to such mathamatical prowess. I used to do maths using words because i hated it so much, then i could make stories.

Naomi
2006-11-06, 07:02 AM
Thanks to everyone who helped, ......... At least the plane isn't landing on a conveyor belt... :)


You only knew that because of the puff of tyre smoke didn't you? :D


Nao