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Math Help - Mechanical Mathematics

  1. #1
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    Mechanical Mathematics

    A diver of mass 60 kg, on entering water with an initial velocity of 15.35 ms-1, experiences a force of resistance, due to the water opposing motion, of magnitude 180v Newtons, where v is the velocity of the diver in ms-1. In addition to the force of gravity, the diver also experiences a constant upward buoyancy force of 720 N. Take the origin of motion to be at the surface of the water. The magnitude g of the acceleration due to gravity can be taken as 10 ms-1.

    Calculate the maximum depth, in metres, the diver will submerge. Give your answer to 3 decimal places.

    The answer is 4.41. Can anyone show me the workings? :'(



    Rgds, Bruce
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    Re: Mechanical Mathematics

    Quote Originally Posted by weijing85 View Post
    A diver of mass 60 kg, on entering water with an initial velocity of 15.35 ms-1, experiences a force of resistance, due to the water opposing motion, of magnitude 180v Newtons, where v is the velocity of the diver in ms-1. In addition to the force of gravity, the diver also experiences a constant upward buoyancy force of 720 N. Take the origin of motion to be at the surface of the water. The magnitude g of the acceleration due to gravity can be taken as 10 ms-1.

    Calculate the maximum depth, in metres, the diver will submerge. Give your answer to 3 decimal places.

    The answer is 4.41. Can anyone show me the workings? :'(



    Rgds, Bruce
    I'm going to set upward to be the positive (vertical) direction.

    As always we set \Sigma F = ma

    Just about everything is pointed upward save the weight.

    \Sigma F = -w + B + R = -mg + 720 + 180v = ma

    From here you can calculate the acceleration. You've got an initial velocity and an acceleration. How do you find the greatest depth from here?

    -Dan
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  3. #3
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    Re: Mechanical Mathematics

    Hi dan, can give me some more hints...i still cant get it.
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    Re: Mechanical Mathematics

    find the acceleration (deceleration) as indicated by -Dan and then apply the Uniform Decelaration formula to find the total space (depth) travelled..
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    Re: Mechanical Mathematics

    I calculated the acceleration is 5. Am i right?
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