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Math Help - Trig related rates

  1. #1
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    Trig related rates

    A hemi-spherical swimming pool has a radius of 10 metres and is completely full of water. A stone is dropped into the pool, at the centre of the surface of the water, and falls vertically at a constant rate of one metre every five seconds. A light at the edge of the pool casts a shadow of the stone on the opposite side of the pool, as shown in the accompanying diagram. Find the rate at which the shadow is moving along the side of the pool at the instant when the stone lies at a depth of 5 metres. [HINT: You may use the fact that, in the accompanying diagram,θ = 2α .]


    Attempt to solution:

    I am stuck on how do l make up the relation or equation for this problem. Any tips and advise will be greatly appreciated.


    ( Guys l am sorry for posting so much on one day l got an exam tomorrow so l am just doing questions from previous exam papers)
    Attached Thumbnails Attached Thumbnails Trig related rates-related-rates.jpg  
    Last edited by nyasha; April 19th 2009 at 05:05 PM.
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by nyasha View Post
    A hemi-spherical swimming pool has a radius of 10 metres and is completely full of water. A stone is dropped into the pool, at the centre of the surface of the water, and falls vertically at a constant rate of one metre every five seconds. A light at the edge of the pool casts a shadow of the stone on the opposite side of the pool, as shown in the accompanying diagram. Find the rate at which the shadow is moving along the side of the pool at the instant when the stone lies at a depth of 5 metres. [HINT: You may use the fact that, in the accompanying diagram,θ = 2α .]


    Attempt to solution:

    I am stuck on how do l make up the relation or equation for this problem. Any tips and advise will be greatly appreciated.


    ( Guys l am sorry for posting so much on one day l got an exam tomorrow so l am just doing questions from previous exam papers)
    Any way to post the diagram that was given? Or if you can verbally explain where the light is and what angle theta is referring to?
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  3. #3
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    Quote Originally Posted by mollymcf2009 View Post
    Any way to post the diagram that was given? Or if you can verbally explain where the light is and what angle theta is referring to?
    I have added the diagram. I totally forgot
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