Calculus Minimum Distance Question. Plz Help

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mathnerd

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At 11:00 AM, a 747 Jet is traveling east to 800 km/h. At the same instant, a DC48 is 45 km east and 90 km north of the 747. It is at the same altitude traveling 600 km/h. What is the closest distance of approach of the planes, and at what time does it occur?

I have the diagram drawn here:[attachment=0:dap00h6m]newpiz.JPG[/attachment:dap00h6m]

Now, I understand that to find d, the formula is \(\displaystyle \sqrt{45^2+x^2}\)

So d = \(\displaystyle \sqrt{45^2+(90-x)^2}\)

And the other vertical distance is 90-x. I know that I have to add these two up to get the total distance between the two planes. But I don't understand how to do this. Please tell me if I am understanding the question correctly.

Thanks.
 

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The distance the 747 travels is 800t. Therefore, it's distance from the origin is 45-800t

The DC48 has a distance from the origin of 90-600t. I assume the DC48 is traveling south.

So, the distance between them is \(\displaystyle S=(45-800t)^{2}+(90-600t)^{2}\)

The distance and square of the distance have their max and min at the same points, so you do not have to differentiate the radical.

Differentiate, set to 0 and solve for t.
 
I am confused. Do you mean "t" is the time?

Also, why is that the distance and square of the distance have same max/min points? Also, why do we have to square the distance?

Edit, if I differentiate, I get t = 0.09

Please clarify this bit for me. I need to know how S formula was made. Thanks.
 
I hope you know Pythaogras. That's all it is. I assumed you knew. Also, distance = rate times time, d=rt.

Nothing fancy.
 
Ok. After differentiating, putting distance`=0, then finding for t. Then I went and put the t back into distance formula. Then, it came to be 2025 km. So would I have to square root 2025? Also, please give some hint regarding what time do I put as to when this distance is available. Thanks.
 
Thank you very much. I was waiting for that confirmation. Once again Dr. Flim-Flam, you have come to save the day. lol.

Thanks.
 
mathnerd said:
I was waiting for that confirmation.
Click to expand...
In future, when you've worked the exercise all the way to the end (progress of which your earlier posts gave no indication), kindly please show that. Thank you.

Eliz.
 
You are correct with the t=9/100. But this is 9/100 hrs. In minutes \(\displaystyle \frac{9}{100}(60)=5.4\)

the time is 5 minutes and 24 seconds past 11:00 am.
 
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