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- Thread starter dinogal
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The altitude and horizontal distance form a right triangle with the distance as the hypotenuse, so

\(\displaystyle D = \sqrt{A^2 + H^2}\)

To find how fast the distance changes with time, take the derivative with respect to time \(\displaystyle t\). Also, note that \(\displaystyle A\) never changes, so \(\displaystyle dA/dt = 0\)

\(\displaystyle \frac{dD}{dt} = \frac{1}{2}(A^2 + H^2)^{-\frac{1}{2}}(2H\frac{dH}{dt})\)

The question asks for the value of \(\displaystyle \frac{dD}{dt}\) when \(\displaystyle H\) is 2 miles, and \(\displaystyle dH/dt\) is 50 mi / hr.

- Jan 26, 2012

- 890

What do you mean by when it is 2 mi away from the station, is this the horizontal distance, or the slant range. As it is written the usual assumption would be slant range but I see that at least one other poster has assumed it is the plan range (horizontal distance).So a plane flying horizontally at an altitude of 1 mi and a speed of 50 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

CB

PS: To the USA in general , and partially to the UK for that matter, smarten up and stop using customary/imperial units, you only confuse yourselves when having to convert between customary units and metric.

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I wish we would. I have hoped for this since the early 70s when a partial effort was made here, but I was a child at that time and I remember the prevailing attitude among the adults was that the metric system was somehow un-American (as if the system we do use is). Alas, the meager effort was abandoned, and we have been steadfastly stubborn ever since. Maybe another effort will be made here within the next century....

PS: To the USA in general , and partially to the UK for that matter, smarten up and stop using customary/imperial units, you only confuse yourselves when having to convert between customary units and metric.

- Jan 26, 2012

- 890

The education system could make a start by not setting homework problems in customary units.I wish we would. I have hoped for this since the early 70s when a partial effort was made here, but I was a child at that time and I remember the prevailing attitude among the adults was that the metric system was somehow un-American (as if the system we do use is). Alas, the meager effort was abandoned, and we have been steadfastly stubborn ever since. Maybe another effort will be made here within the next century.

CB

- Oct 16, 2012

- 126

A very good example is speed, I know that 80kph is about 50mph... I believe... Most Americans would have no idea...

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