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Math Help - Determining the speed

  1. #1
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    Determining the speed

    A light house facing north sends out a fan shaped beam of light extending from north east to north west. An observer on a steamer , sailing due west ,first sees the light when he is 5 km away from the lighthouse and continues to see it for 30\sqrt2minutes.What is the speed of the steamer?
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  2. #2
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    Quote Originally Posted by jashansinghal View Post
    A light house facing north sends out a fan shaped beam of light extending from north east to north west. An observer on a steamer , sailing due west ,first sees the light when he is 5 km away from the lighthouse and continues to see it for 30\sqrt2minutes.What is the speed of the steamer?
    Hi jashansinghal,

    In crossing the fan of light, the steamer will have travelled

    \sqrt{5^2+5^2}=\sqrt{25+25}=\sqrt{50}\ km

    using Pythagoras' theorem.

    t=30\sqrt{2}\ minutes=\frac{30\sqrt{2}}{60}\ hours=\frac{\sqrt{2}}{2}\ hours

    av.\ speed=\frac{distance}{time}=\frac{\sqrt{50}}{\left  (\frac{\sqrt{2}}{2}\right)}

    =\frac{2\sqrt{50}}{\sqrt{2}}=\frac{\sqrt{50}\sqrt{  2}\sqrt{2}}{\sqrt{2}}

    =\sqrt{50}\sqrt{2}=\sqrt{2(50)}=\sqrt{100}= 10 km per hour
    Attached Thumbnails Attached Thumbnails Determining the speed-lighthouse.jpg  
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