HELP MATHS PROBLEM need really smart maths people

[iridemymuni]

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]

Originally Posted by iridemymuni

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]

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]

Originally Posted by ivan

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]

Originally Posted by iridemymuni

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]

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]

Originally Posted by Dave Coleman

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]

Originally Posted by iridemymuni

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]

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]

Originally Posted by ivan

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]

Originally Posted by iridemymuni

. 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]

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]

Originally Posted by iridemymuni

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]

it said it was a constant lol :s.

please help with the log thing. please please please

[ivan]

Originally Posted by iridemymuni

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