Author Topic: Application Diff (Read 559 times) Tweet Share

moneran · « **on:** June 17, 2010, 07:36:28 pm »

An aeroplane is flying horizonatally at a constant height of 1000m. At certain instant the angle of elevation is 30⁰ and decreasing and the speed of the aeroplane is 480 kmph
a) hw fast is the angle decrasing at this instant ?
answer in degrees/s
b)how fast is the distance between the aeroplane and the observation point changing at this instant?
essentials pg 402 question 2
Ex11g

the.watchman · « **Reply #1 on:** June 17, 2010, 07:44:42 pm »

Let the angle be $\theta$
Let the horizontal distance from the point of observation to the plane be $x$ km

Then $\tan \theta = \frac{1000}{x}$

$x=\frac{1000}{\tan \theta}$

$\frac{dx}{d\theta}=-\frac{1000}{\sin ^2 \theta}$

Using the chain rule: $\frac{d\theta}{dt}=\frac{d\theta}{dx} \cdot \frac{dx}{dt}$

So $\frac{d\theta}{dt}=-\frac{\sin ^2 \theta}{1000} \cdot (-480)$

sub in $\theta = \frac{\pi}{6}$ to get rate

For this one, define another variable as the distance between the plane and the observation point and use a similar method

moneran · « **Reply #2 on:** June 17, 2010, 08:03:20 pm »

Can anyone do question 4 on ex 11G essentials pg 402

the.watchman · « **Reply #3 on:** June 17, 2010, 08:37:40 pm »

Quote from: moneran on June 17, 2010, 08:03:20 pm

Can anyone do question 4 on ex 11G essentials pg 402

Sorry I would but I don't often bring my textbook home...

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