related rates airplane expample.

mags22

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Oct 7, 2021
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An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the airplane?
 

mmm4444bot

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Hello. Are far did you get? Please explain where you're stuck. Thank you!

🤖
 

HallsofIvy

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You did not say what "distance s" means! Is it the distance between the airplane and the radar antenna? If so, since the antenna is fixed on the ground, isn't the ground speed of the airplane exactly what the radar is giving?
 

Dr.Peterson

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You did not say what "distance s" means! Is it the distance between the airplane and the radar antenna? If so, since the antenna is fixed on the ground, isn't the ground speed of the airplane exactly what the radar is giving?
No, I think it's like this:

1633972514679.png

We know ds/dt, we want dx/dt.

@mags22, what ideas have you had? Can you write an equation relating x and s?
 
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