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January 28, 2015

January 28, 2015

Posted by **Heather** on Friday, November 25, 2011 at 9:49pm.

- Calculus -
**drwls**, Friday, November 25, 2011 at 10:04pmIt depends upon the angle that the shore makes with the beam.

What is x ?

An illustration is needed for me to make sense of this question.

- Calculus -
**Reiny**, Friday, November 25, 2011 at 10:23pmI recall seeing this type of question before, and I will assume it is the standard type.

Usually we are to find the speed of the light as it moves along the shore.

Draw a perpendicular line from the lighthouse to the shore.

Let the angle between the line to the shore and the beam of light be Ø , and let the light rotate counterclockwise.

dØ/dt = 4 (2π) radians/minute = 8π rad/min

Let the beam of light be x miles along the shore

tanØ = x/.5

x = .5tanØ

dx/dt = .5 sec^2 Ø dØ/dt

when x = .25

tanØ = .25/.5 = 1/2

cosØ = 2/√5

secØ = √5/2

sec^2 Ø = 5/4

dx = .5(5/4)(8π) miles/min = 5π miles/minute

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