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Related rates, check my answer pls

  • #1
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Homework Statement


A highway patrol plane is flying 1 mile above a long, straight road, with constant ground speed of 120 m.p.h. Using radar, the pilot detects a car whose distance from the plane is 1.5 miles and decreasing at a rate of 136 m.p.h. How fast is the car traveling along the highway?


The Attempt at a Solution



work.jpg

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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It's wrong. The value of x in the related rates equation is not an unknown. x^2+1=1.5^2. It's easy to find. And 'x' is the distance, not a velocity. dx/dT is not -120. It's a combination of the plane's velocity with the unknown velocity of the car. That's what you want to solve for.
 
Last edited:
  • #3
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So would you say that (velocity of car)[itex]\frac{dc}{dt} = 120 + \frac{dx}{dt}[/itex]

so that

[itex]\frac{dh}{dt}=\frac{x}{\sqrt{x^2+1}}\frac{dx}{dt}[/itex]

where

[itex]\frac{dx}{dt} = \frac{dc}{dt} - 120[/itex]

[itex]\frac{dh}{dt}= -136[/itex]

and

x=[itex]\sqrt{1.25}[/itex]

so that [itex]\frac{dc}{dt} \approx -62.46 \approx 62.46 mph[/itex]
 
Last edited:
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
So would you say that (velocity of car)[itex]\frac{dc}{dt} = 120 + \frac{dx}{dt}[/itex]

so that

[itex]\frac{dh}{dt}=\frac{x}{\sqrt{x^2+1}}\frac{dx}{dt}[/itex]

where

[itex]\frac{dx}{dt} = \frac{dc}{dt} - 120[/itex]

[itex]\frac{dh}{dt}= -136[/itex]

and

x=[itex]\sqrt{1.25}[/itex]

so that [itex]\frac{dc}{dt} \approx -62.46 \approx 62.46 mph[/itex]
Yes, I think that's more like it.
 

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