September 17th, 2015, 10:08 PM  #1 
Newbie Joined: Sep 2015 From: mexico Posts: 10 Thanks: 0  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 10:37 PM. 
September 18th, 2015, 04:56 AM  #2 
Newbie Joined: Sep 2015 From: Uk Posts: 4 Thanks: 1 
I had a go but might be wrong Last edited by Jtatezen; September 18th, 2015 at 04:59 AM. 
September 18th, 2015, 06:45 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,770 Thanks: 1424 
$\theta = \arctan(2x)$ $\dfrac{d\theta}{dt} = \dfrac{2}{1+4x^2} \cdot \dfrac{dx}{dt}$ 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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angle, changing, problem, searchlight 
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