# calculus

posted by .

(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:

(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

## Similar Questions

1. ### physics

What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/22 of its value at the Earth's surface?
2. ### physics

What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/45 of its value at the Earth's surface?
3. ### phy

What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/12 of its value at the Earth's surface?
4. ### Physics

What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/20 of its value at the Earth's surface?
5. ### Physics

A. Use the relation 2 m m m GM g R ƒ­ to find the acceleration due to gravity on the surface of the Moon. You can use the following data: Mass of the Moon m M = 7.35 ¡Ñ 1022 kg. Radius of the Moon m R = 1.74 ¡Ñ 106 m. B. How …
6. ### precalculus

The acceleration acting on a falling object due to gravity varies inversely with the square of the object's distance from the center of Earth. At the surface of Earth, where x = 1 Earth radius, the acceleration is y = 9.8 m/s2 1. Use …
7. ### physics

If the earth acceleration due to gravity on a mass of 2000kg on the earth surface is 10ms.What will be the acceleration due to gravity when it is at a point twice the radius of the earth.What is the gravitational force on it.