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Thread: 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 $\displaystyle 30\sqrt2$minutes.What is the speed of the steamer?
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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 $\displaystyle 30\sqrt2$minutes.What is the speed of the steamer?
    Hi jashansinghal,

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

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

    using Pythagoras' theorem.

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

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

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

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