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September 17th, 2015, 11:08 PM   #1
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searchlight changing angle problem

Problem says: a searchlight on a patrolboat sited 1/2km offshore, follows a dune buggy that moves parallel to the water along a straight beach. The dune buggy is traveling at a constant rate of 15km/hour. Use an inverse trigonometric function to determine the rate at which the searchlight is rotating when the dune buggy is 1/2km from the point on the shore nearest to the boat.

Please help solve and develop by steps to understand.

Last edited by skipjack; September 17th, 2015 at 11:37 PM.
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September 18th, 2015, 05:56 AM   #2
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I had a go but might be wrong

Last edited by Jtatezen; September 18th, 2015 at 05:59 AM.
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September 18th, 2015, 07:45 AM   #3
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$\theta = \arctan(2x)$

$\dfrac{d\theta}{dt} = \dfrac{2}{1+4x^2} \cdot \dfrac{dx}{dt}$

when the buggy is 1/2 km from shore, $x=0$ ...

$\dfrac{d\theta}{dt} = 2 \cdot 15 = 30 \text{ rad/hr}$
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