What is the speed of the lighthouse beam along the shoreline?

[Feodalherren]

Homework Statement

A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam moving along the shoreline when it is 1km from P?

Homework Equations

The Attempt at a Solution

I drew a picture and got a triangle out of it. I labeled the center angle θ and a straight line from P that's 1km long as X.

Tan θ = x/3


Want dx/dt when dθ/dt = 24∏

correct?
The reasoning was that
C = 2∏r

r=3

C=6∏ but 4 revolutions/min gives me 24∏.

I get dx/dt = 80∏ as the solution, that seems way too fast.

 

[berkeman]

∏

Homework Statement

A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam moving along the shoreline when it is 1km from P?

Homework Equations

The Attempt at a Solution

I drew a picture and got a triangle out of it. I labeled the center angle θ and a straight line from P that's 1km long as X.

Tan θ = x/3


Want dx/dt when dθ/dt = 24∏

correct?
The reasoning was that
C = 2∏r

r=3

C=6∏ but 4 revolutions/min gives me 24∏.

I get dx/dt = 80∏ as the solution, that seems way too fast.

4 revolutions per minute gives 2∏ radians per 15 seconds. What does that give you for ω in units of radians per second?

 

[Feodalherren]

Hmm I'm not following... Could you tell me how you arrived at that?