SOLUTION: The gravitational forc between two objects varies inversely as the square of the distance between the objects. If a force of 25 pounds results from two objects that are 6 miles apa

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Question 128722This question is from textbook Fundamentals of Algebric Modeling
: The gravitational forc between two objects varies inversely as the square of the distance between the objects. If a force of 25 pounds results from two objects that are 6 miles apart, ow much force results from the two objects that are 15 miles apart?
my answer is 30 pounds of force This question is from textbook Fundamentals of Algebric Modeling

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, the gravitational between two objects varies inversely as the square of the distance between them, so you can see that as the objects get farther apart, the force between them diminishes, right?
So your answer of 30 pounds of force when the objects are 15 miles apart is not reasonable given that the force is 25 pounds when the objects are only 6 miles apart! The force should be less when they are farther apart!
First, write the equation of variation:
F+=+k%2Fd%5E2 where k is the constant of variation.
You are given that the force (F)is 25 pounds when the objects are at a distance (d) of 6 miles. Substitute these values into the equation to find the value of k.
25+=+k%2F6%5E2
25+=+k%2F36 Multiply both sides by 36.
900+=+k This is the value of the constant of variation, k.
Now you can rewtite the equation as:
F+=+900%2Fd%5E2 Substitute d = 15 miles.
F+=+900%2F%2815%29%5E2
F+=+900%2F225
F+=+4pounds.