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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Boots on September 06, 2011, 02:26:37 pm

Title: related rates
Post by: Boots on September 06, 2011, 02:26:37 pm: Hi guys, I am unsure as to which angle equation I should use to solve this, please help

A train is travelling at 15km/hr along a straight track. A fixed movie camera, 500m away from the track is focused on the train.
How fast is the camera rotating (in radians/hour) at the moment when the train is 1km from the camera?
Title: Re: related rates
Post by: Boots on September 06, 2011, 05:46:55 pm: anyone?
Title: Re: related rates
Post by: luken93 on September 06, 2011, 06:54:43 pm: $frac{d \theta}{dt} = \frac{dx}{dt} \times \frac{d \theta}{dx}$

Since dx\dt = velocity = 15 km/hr
$tan ( \theta) = \frac{x}{500}$ => $x = 500 tan( \theta)$
$\frac{dx}{d \theta} = 500 sec^2( \theta)$

$frac{d \theta}{dt} = 15 \times \frac{1}{500 sec^2( \theta)}$

Now, when hypotenuse = 1000, the angle is arccos(500/1000) = pi/3

$\therefore frac{d \theta}{dt} = 15 \times \frac{1}{500 sec^2(\pi/3)}$

Hopefully this is right :P