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Math Help - Power function question?

  1. #1
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    Exclamation Power function question?

    A person's weight, w, on a planet of radius d is given by
    w = kd^-2, k > 0
    where the constant k depends on the masses of he person and the planet.

    a) A man weights 180 pounds on the surface of the earth. How much does he weigh on the surface of a planet whose mass is the same earth's, but whose radius is three times as large? One-third as large?

    b) What fraction of the earth's radius must an equally massive planet have if, on this planet, the weight of the man in part (a) is one ton?




    I need help with part b). How would we solve this problem?

    Would we place w = 2000d^-2 and w = 180d^-2? Thank you.
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by nox16 View Post
    A person's weight, w, on a planet of radius d is given by
    w = kd^-2, k > 0
    where the constant k depends on the masses of he person and the planet.

    a) A man weights 180 pounds on the surface of the earth. How much does he weigh on the surface of a planet whose mass is the same earth's, but whose radius is three times as large? One-third as large?

    b) What fraction of the earth's radius must an equally massive planet have if, on this planet, the weight of the man in part (a) is one ton?




    I need help with part b). How would we solve this problem?

    Would we place w = 2000d^-2 and w = 180d^-2? Thank you.
    his weight at the earth 180 pounds
    on other plant his weight 1000 pounds this plant have same massive as earth

    180 = \frac{k}{d^2_e}

    k =180(d^2_e)

    1000 = \frac{k}{d^2_p}

    k = 1000(d^2_p)

    180(d^2_e) = 1000(d^2_p)

    \frac{d^2_e}{d^2_p} = \frac{1000}{180}

    \frac{d_e}{d_p}= \sqrt{\frac{1000}{180}}

    \frac{d_e}{d_p} = \sqrt{\frac{100}{18}} = \frac{10}{3\sqrt{2}}

    that what they ask for in b)
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