calculus

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(1 pt) The acceleration due to gravity, g, is given by
g = (G*M)/(r^2)

where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant.

(a) Suppose that we change from our distance from the center of the Earth by a distance \Delta r = x. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration:

(Your answer will be a function of x and r.)

(b) Is this change positive or negative?

(c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.29 km; assume the radius of the Earth is 6400 km)?
percent change =

  • calculus -

    a) -2(x/r)
    b) Negative
    c) 2(4.29 / 6400) * 100

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