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Author Topic: Related Rates, looking at an aeroplane  (Read 2352 times)  Share 

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Related Rates, looking at an aeroplane
« on: June 19, 2008, 06:37:02 pm »
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An aeroplane is flying horizontally at a constant height of 1000m. At a certain instant the angle of elevation is and decreasing and the speed of the aeroplane is 480 km/h.

a) How fast is decreasing at this instant? (Answer in degrees/s.)

b) How fast is the distance between the aeroplane and the observation point changing at this instant?

I can't get A) :( I keep getting the angle in terms of a trig expression, not an inverse trig expression or etc. Thanks

dcc

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Re: Related Rates, looking at an aeroplane
« Reply #1 on: June 19, 2008, 06:47:16 pm »
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Let h = horizontal displacement, so .

We are looking for

Now lets connect h and theta:





When theta is 30 degrees:



« Last Edit: June 19, 2008, 07:02:53 pm by dcc »

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Re: Related Rates, looking at an aeroplane
« Reply #2 on: June 19, 2008, 06:52:29 pm »
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Thanks dcc! I looks like I forgot to convert to m/s :S

Still though, if you put in radians, wouldn't the result still give the answer in degrees/second?
« Last Edit: June 19, 2008, 06:54:05 pm by DivideBy0 »

dcc

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Re: Related Rates, looking at an aeroplane
« Reply #3 on: June 19, 2008, 06:53:51 pm »
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If you are interested, there was a question almost exactly like this last years Specialist Maths exam two (except I think the height was changing, rather than the horizontal displacement).

dcc

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Re: Related Rates, looking at an aeroplane
« Reply #4 on: June 19, 2008, 07:01:33 pm »
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Thanks dcc! I looks like I forgot to convert to m/s :S

Still though, if you put in radians, wouldn't the result still give the answer in degrees/second?

Indeed, this complicates the matter slightly, so the answer is gave is incorrect, as you will have to convert from -1/30 radians/second to degrees/second (as the derivative of trig functions for an angle in degrees is different to that of an angle in radians).



I think this should be the answer, though I am not 100% sure.
« Last Edit: June 19, 2008, 07:04:15 pm by dcc »

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Re: Related Rates, looking at an aeroplane
« Reply #5 on: June 19, 2008, 07:04:02 pm »
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thanks, I just confirmed with the book that is correct