# Science:Math Exam Resources/Courses/MATH102/December 2019/Question 10(b)

MATH102 December 2019

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### Question 10(b)

A lighthouse is 1 km from the shore. Its beam rotates, taking 20 seconds for one full revolution. In the diagram at right, the dotted line is the beam of light; the solid line is the shortest line from the lighthouse to the shore; and ${\displaystyle \theta }$ is the angle between those two lines.

(b) As the light beam turns, the point where it hits the shore moves. How fast is that point moving along the shoreline at the instant when it is closest to the lighthouse (when ${\displaystyle \theta =0}$)? Give your answer in km/sec.

UBC Math 102 2019 Q10
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