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

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MATH102 December 2019
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Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.


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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 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 )? Give your answer in km/sec.

UBC Math 102 2019 Q10

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!


Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

  • If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
  • If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.





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