SOLUTION: Hint for this assignment: Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for yo

Question 161485: Hint for this assignment: Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions.
1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: w=Cr^-2 , where C is a constant, and r is the distance that the object is from the center of the earth.
a. Solve the equation for r.
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
c. Use the value of C you found in the previous question to determine how much the object would weigh in
i. Death Valley (282 feet below sea level)
ii. The top of Mt McKinley (20,320 feet above sea level)

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: w=Cr^-2 , where C is a constant, and r is the distance that the object is from the center of the earth.
:
a. Solve the equation for r.
w = Cr^-2
:
w = :Reciprocal makes the exponent positive
:
wr^2 = C; multiply both sides by r^2
:
r^2 = ; divide both sides by w
r =
:
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.)
Use the equation: C = wr^2
C = 100*3963^2
C = 1,570,536,900
:
:
c. Use the value of C you found in the previous question to determine how much the object would weigh in
:
i. Death Valley (282 feet below sea level)
w = Cr^-2
w = 1,570,536,900 * (3963-)^-2
w = 1,570,536,900 * (3963 - .0534)^-2
w = 1,570,536,900 * (3962.9456)^-2
w = 1,570,536,900 * 6.374(10^-8)
w = 100.0027 lb
:
:
ii. The top of Mt McKinley (20,320 feet above sea level)
w = 1,570,536,900 * (3963+)^-2
w = 1,570,536,900 * (3962 + 3.845)^-2
w = 1,570,536,900 * (3966.8485)^-2
w = 1,570,536,900 * 6.3549(10^-8)
w = 99.8 lb
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