2324 A variable y is said to be inversely proportional to the square of a variable x if

Chapter 0, Problem 24

(choose chapter or problem)

2324 A variable y is said to be inversely proportional to the square of a variable x if y is related to x by an equation of the form y = k/x2, where k is a nonzero constant, called the constant of proportionality. This terminology is used in these exercises. It follows from Newtons Law of Universal Gravitation thatthe weight W of an object (relative to the Earth) is inverselyproportional to the square of the distance x between theobject and the center of the Earth, that is, W = C/x2.(a) Assuming that a weather satellite weighs 2000 poundson the surface of the Earth and that the Earth is a sphereof radius 4000 miles, find the constant C.(b) Find the weight of the satellite when it is 1000 milesabove the surface of the Earth.(c) Make a graph of the satellites weight versus its distancefrom the center of the Earth.(d) Is there any distance from the center of the Earth atwhich the weight of the satellite is zero? Explain yourreasoning.