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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