The speed of the water in a whirlpoil varies inversely with the radius. if the water speed is 2.5 feet per second at a radius of 30 feet wha

Question

The speed of the water in a whirlpoil varies inversely with the radius. if the water speed is 2.5 feet per second at a radius of 30 feet what js the speed of the water at a radius of 3 feet?​

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Ben Gia 5 months 2021-08-10T20:42:33+00:00 1 Answers 39 views 0

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  1. Edana
    -1
    2021-08-10T20:44:08+00:00
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    Answer:

    25 feet per second.

    Step-by-step explanation:

    Let s represent the speed of the water and r represent the radius of the whirlpool.

    The speed in a whirlpool varies inversely with the radius. Therefore, we can write that:

    \displaystyle s=\frac{k}{r}

    Where k is the constant of variation.

    We know that the speed is 2.5 feet per second when the radius is 30 feet.

    So, s = 2.5 when r = 30. Substitute:

    \displaystyle 2.5=\frac{k}{30}

    Solve for k:

    k=30(2.5)=75

    So, our equation is:

    \displaystyle s=\frac{75}{r}

    Then when the radius is three feet, r = 3. Evaluate for s:

    \displaystyle s=\frac{75}{(3)}=25\text{ feet per second}

    So, the speed of the water in a whirlpool with a radius of three feet is 25 feet per second.

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