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values of y and theta

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The attached diagram shoes a lighthouse, L, 4.2 km from the nearest point, S, on a straight shoreline. The lighthouse beam rotates with a constant period of one complete rotation every 40 seconds. The beam makes an angle of theta with the line LS and the beam hits the shoreline a distance y km from S.

At what rate is the beam moving along the shore line when:
a) Theta=pi/6
b) y=10 km

What are the values of y and theta when the beam moves along at 3*10^5 km/s?

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Solution Summary

The expert determines the values of y and theta from this case.

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We need dy/dt. But y=4.2*tan(theta) so substituting this into y in dy/dt we get

dy/dt=4.2*d[tan(theta)]/dt=4.2*(1+tan^2(theta))*d(theta)/dt .

Now d(theta)/dt=w=2*pi/T where w is angular velocity and T is the period.
So ...

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