Rotating Lighthouse Beacon Problem: Figure 3-3h shows a lighthouse 500 m from the shore

Chapter 3, Problem 15

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Rotating Lighthouse Beacon Problem: Figure 3-3h shows a lighthouse 500 m from the shore. Figure 3-3h A rotating light on the top of the lighthouse sends out light beams in opposite directions. As the beacon rotates through an angle , a spot of light moves along the shore. Let L be the length of the light beam from the lighthouse to the spot on the shore. Let D be the directed distance along the shore to the spot of light; that is, D is positive to the right if youre on the shore facing the lighthouse and negative to the left. b. When = 55, where does the spot of light hit the shore? How long is the light beam? c. What is the first positive value of for which the light beam will be 2000 m long? d. Explain why D is negative for 90 < < 180 and for 270 < < 360 and why L is negative for 90 < < 270. e. Explain the physical significance of the asymptote in each graph at = 90.