
#1
March 27th, 2020,
01:47
A lighthouse is located on a small island 16 km offshore from the nearest point P on a straight shoreline. Its light makes 5 revolutions per minute. How fast is the light beam moving along the shoreline when it is shining on a point 3 km along the shoreline from P?

March 27th, 2020 01:47
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#2
March 27th, 2020,
09:04
$\dfrac{d\theta}{dt}$ = 5 rpm = $\dfrac{10\pi}{60 \, sec} = \dfrac{\pi}{6}$ rad/sec
consider the right triangle formed by the light beam, the shoreline, and the perpendicular distance from the light house to the shoreline (recommend you make a sketch)
let $\theta$ be the angle between the light beam and the perpendicular distance, and $x$ be the distance from where the light beam intersects the shoreline to where the perpendicular distance segment intersects the shoreline. You are given the fixed perpendicular distance.
Using the aforementioned right triangle, write a trig equation that relates $x$, $\theta$, and the 16 km distance.
Take the time derivative of the equation and determine $\dfrac{dx}{dt}$ when $x=3$ km.
Mind your units.
Last edited by skeeter; March 27th, 2020 at 09:48.