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Math Help - Question about Application of Calculus II

  1. #1
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    Question about Application of Calculus II

    I have a project to do and I'm simply at a loss.
    We have to find two applications of Calculus II in the construction of a sailboat; but our teacher already gave the example of calculating volume (in order for the boat to float)

    I've looked it up but I have trouble finding links.
    I've thought maybe calculating the area of the sail? (Using integrals, calculating the area between two curves)

    Thanks for your consideration!
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  2. #2
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    Quote Originally Posted by Volcanicrain View Post
    I have a project to do and I'm simply at a loss.
    We have to find two applications of Calculus II in the construction of a sailboat; but our teacher already gave the example of calculating volume (in order for the boat to float)

    I've looked it up but I have trouble finding links.
    I've thought maybe calculating the area of the sail? (Using integrals, calculating the area between two curves)

    Thanks for your consideration!
    Finding the area of the sail is definitely an application of Calculus. You could think of it as integrating between two curves, or if the bottom curve is a flat like a triangular sail, then the integral is even simpler.

    The possibilities are endless; just think a bit.

    Construction of sailboat... what about the speed that the main sail goes up the mast when the bottom edge is a given amount of distance away from the haul of the boat?

    Personally, I think the mechanics of the boats trajectory are important during construction. You can measure velocity and acceleration of the boat given an equation of position dependent upon time and mass of the boat.

    How about some optimization? Suppose you would like to minimize the amount of surface area for the bottom two feet of the boat?

    Hope this has helped!
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  3. #3
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    I'm not so sure I understand the points you've put forward to be honest (I feel kind of dumb!)

    My friend and I found something about the surface area of the bottom of the boat - it has to be of a certain amount for the boat to be able to float in water (if it's too small it would sink).
    Then we found volume - something about if the volume of water that has been displaced when the sail goes in the water, we can thus calculate that of the boat that is in the water...

    I'm really not sure. My teacher sure loves complicated things.

    What's hard though is that we can only refer to integrals, its applications and series - not derivatives X_X
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  4. #4
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    Quote Originally Posted by Volcanicrain View Post
    I'm not so sure I understand the points you've put forward to be honest (I feel kind of dumb!)

    My friend and I found something about the surface area of the bottom of the boat - it has to be of a certain amount for the boat to be able to float in water (if it's too small it would sink).
    Then we found volume - something about if the volume of water that has been displaced when the sail goes in the water, we can thus calculate that of the boat that is in the water...

    I'm really not sure. My teacher sure loves complicated things.

    What's hard though is that we can only refer to integrals, its applications and series - not derivatives X_X
    If it is integrals, then stick to the area of the sail and surface area of the bottom of the boat.
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  5. #5
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    Quote Originally Posted by colby2152 View Post
    If it is integrals, then stick to the area of the sail and surface area of the bottom of the boat.
    My teacher said surface area of bottom of the boat is wrong... this actually makes sense now. Area of the sail is good though.\

    Can you please explain the things you said before?? (Are they related to integrals?)
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