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 Earth.

a. Solve the equation W=Cr^-2 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 Mount McKinley (20,320 feet above sea level).

Additonal information: You many have to convert from feet to miles. Use 1 mile =5,280 for your conversions when needed.

Solution:

(a) r = sqrt(C/W)

(b) C = W*r^2 = 100 pounds *(3963 miles)2 = 1.57*10^9 (pounds*miles^2)

(c)

(i) r = 3963-282 = 3681 miles

 W = 115.91 pounds

So weight is 115.91 pounds

(ii)r = 20320/5280 + 3963 = 3966.84 miles

W = 99.31 pounds

So weight is 99.31 pounds