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Related rates, my answer differs from the book, misprint or me?

How fast is the length of his shadow on the building decreasing when he is 4 m from the buildingRelated Rates: rate of change of the distance between two objectsRelated Rates change in theta

1

$begingroup$

Did my answer go wrong or does the book have a misprint?(there have been some inconstancies between the definitions used in the chapters and answer key, like two different authors, though only one is listed)

The problem: An airplane is flying 500 miles per hour horizontal one mile high over a radar station. Find the rate at which the distance is increasing when the plane is 2 miles from the station.

My answer is $1000/sqrt5$ or $200*sqrt5$

The book gives $250*sqrt3$

My method: triangle abc, a=1, b=2, and c is the hypotenuse, $db/dt=500$, and $c^2=1^2+b^2$, and I want $dc/dt$ at b=2

I took the derivative: $2c*fracdcdt=0+2b*fracdbdt$,

solved for $dc/dt$; $dc/dt=frac2b*db/dt2c$

Substitute the variables; $c=sqrt1+4$ and so $fracdcdt=frac2*2*5002*sqrt5=frac1000sqrt5$

related-rates

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edited 2 days ago

Max Power

asked 2 days ago

Max PowerMax Power

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1

$begingroup$

Did my answer go wrong or does the book have a misprint?(there have been some inconstancies between the definitions used in the chapters and answer key, like two different authors, though only one is listed)

The problem: An airplane is flying 500 miles per hour horizontal one mile high over a radar station. Find the rate at which the distance is increasing when the plane is 2 miles from the station.

My answer is $1000/sqrt5$ or $200*sqrt5$

The book gives $250*sqrt3$

My method: triangle abc, a=1, b=2, and c is the hypotenuse, $db/dt=500$, and $c^2=1^2+b^2$, and I want $dc/dt$ at b=2

I took the derivative: $2c*fracdcdt=0+2b*fracdbdt$,

solved for $dc/dt$; $dc/dt=frac2b*db/dt2c$

Substitute the variables; $c=sqrt1+4$ and so $fracdcdt=frac2*2*5002*sqrt5=frac1000sqrt5$

related-rates

share|cite|improve this question

edited 2 days ago

Max Power

asked 2 days ago

Max PowerMax Power

1085

New contributor

Max Power is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

Did my answer go wrong or does the book have a misprint?(there have been some inconstancies between the definitions used in the chapters and answer key, like two different authors, though only one is listed)

The problem: An airplane is flying 500 miles per hour horizontal one mile high over a radar station. Find the rate at which the distance is increasing when the plane is 2 miles from the station.

My answer is $1000/sqrt5$ or $200*sqrt5$

The book gives $250*sqrt3$

My method: triangle abc, a=1, b=2, and c is the hypotenuse, $db/dt=500$, and $c^2=1^2+b^2$, and I want $dc/dt$ at b=2

I took the derivative: $2c*fracdcdt=0+2b*fracdbdt$,

solved for $dc/dt$; $dc/dt=frac2b*db/dt2c$

Substitute the variables; $c=sqrt1+4$ and so $fracdcdt=frac2*2*5002*sqrt5=frac1000sqrt5$

related-rates

share|cite|improve this question

edited 2 days ago

Max Power

asked 2 days ago

Max PowerMax Power

1085

New contributor

Max Power is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 2 days ago

Max Power

asked 2 days ago

Max PowerMax Power

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Max Power is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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share|cite|improve this question

edited 2 days ago

Max Power

asked 2 days ago

Max PowerMax Power

1085

New contributor

Max Power is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 days ago

Max PowerMax Power

1085

New contributor

Max Power is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 2 days ago

Max PowerMax Power

1085

2 Answers
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1

$begingroup$

It may be a misprint, but I don't think your answer is right either. The question asks for $dc/dt$ when the distance from the station is 2 - this means when c=2 not when b=2. Other than that your answer is correct; plugging a=1, b=$sqrt 3$, c=2 in, I get $250sqrt3$ (not $250/sqrt3$)

share|cite|improve this answer

answered 2 days ago

Ben Ben

263

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$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ah semantics. Probably not the last time they get the better of me. And yes $250/sqrt3$, was a typo on my part, fixed now.
  $endgroup$
  – Max Power
  2 days ago
  
  

  
  
  
  

add a comment | 

1

$begingroup$

You approach is good, you just mixed up $b$ and $c$. When plane is two miles from the station, $c=2$, $b=sqrt3$. So I think the answer should be $250sqrt3$.

share|cite|improve this answer

answered 2 days ago

VasyaVasya

4,0681618

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1

$begingroup$

It may be a misprint, but I don't think your answer is right either. The question asks for $dc/dt$ when the distance from the station is 2 - this means when c=2 not when b=2. Other than that your answer is correct; plugging a=1, b=$sqrt 3$, c=2 in, I get $250sqrt3$ (not $250/sqrt3$)

share|cite|improve this answer

answered 2 days ago

Ben Ben

263

New contributor

Ben is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ah semantics. Probably not the last time they get the better of me. And yes $250/sqrt3$, was a typo on my part, fixed now.
  $endgroup$
  – Max Power
  2 days ago
  
  

  
  
  
  

add a comment | 

1

$begingroup$

It may be a misprint, but I don't think your answer is right either. The question asks for $dc/dt$ when the distance from the station is 2 - this means when c=2 not when b=2. Other than that your answer is correct; plugging a=1, b=$sqrt 3$, c=2 in, I get $250sqrt3$ (not $250/sqrt3$)

share|cite|improve this answer

answered 2 days ago

Ben Ben

263

New contributor

Ben is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Ah semantics. Probably not the last time they get the better of me. And yes $250/sqrt3$, was a typo on my part, fixed now.
  $endgroup$
  – Max Power
  2 days ago
  
  

  
  
  
  

add a comment | 

$begingroup$

It may be a misprint, but I don't think your answer is right either. The question asks for $dc/dt$ when the distance from the station is 2 - this means when c=2 not when b=2. Other than that your answer is correct; plugging a=1, b=$sqrt 3$, c=2 in, I get $250sqrt3$ (not $250/sqrt3$)

share|cite|improve this answer

answered 2 days ago

Ben Ben

263

New contributor

Ben is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this answer

answered 2 days ago

Ben Ben

263

New contributor

Ben is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 2 days ago

Ben Ben

263

New contributor

Ben is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 2 days ago

Ben Ben

263

1

$begingroup$

You approach is good, you just mixed up $b$ and $c$. When plane is two miles from the station, $c=2$, $b=sqrt3$. So I think the answer should be $250sqrt3$.

share|cite|improve this answer

answered 2 days ago

VasyaVasya

4,0681618

$endgroup$

add a comment | 

1

$begingroup$

You approach is good, you just mixed up $b$ and $c$. When plane is two miles from the station, $c=2$, $b=sqrt3$. So I think the answer should be $250sqrt3$.

share|cite|improve this answer

answered 2 days ago

VasyaVasya

4,0681618

$endgroup$

add a comment | 

$begingroup$

You approach is good, you just mixed up $b$ and $c$. When plane is two miles from the station, $c=2$, $b=sqrt3$. So I think the answer should be $250sqrt3$.

share|cite|improve this answer

answered 2 days ago

VasyaVasya

4,0681618

$endgroup$

share|cite|improve this answer

answered 2 days ago

VasyaVasya

4,0681618

answered 2 days ago

VasyaVasya

4,0681618

answered 2 days ago

VasyaVasya

4,0681618