Question 128722
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/d^2}}} 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/6^2}}}
{{{25 = k/36}}} 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/d^2}}} Substitute d = 15 miles.
{{{F = 900/(15)^2}}}
{{{F = 900/225}}}
{{{F = 4}}}pounds.