How Fast is the Car Traveling Along the Highway?

[e^(i Pi)+1=0]

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

 

[Dick]

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.

 

[e^(i Pi)+1=0]

So would you say that (velocity of car)\frac{dc}{dt} = 120 + \frac{dx}{dt}

so that

\frac{dh}{dt}=\frac{x}{\sqrt{x^2+1}}\frac{dx}{dt}

where

\frac{dx}{dt} = \frac{dc}{dt} - 120

\frac{dh}{dt}= -136

and

x=\sqrt{1.25}

so that \frac{dc}{dt} \approx -62.46 \approx 62.46 mph

 

[Dick]

So would you say that (velocity of car)\frac{dc}{dt} = 120 + \frac{dx}{dt}

so that

\frac{dh}{dt}=\frac{x}{\sqrt{x^2+1}}\frac{dx}{dt}

where

\frac{dx}{dt} = \frac{dc}{dt} - 120

\frac{dh}{dt}= -136

and

x=\sqrt{1.25}

so that \frac{dc}{dt} \approx -62.46 \approx 62.46 mph

Yes, I think that's more like it.