The weight of an object follows the equation w=Cr^-2, where C is the constant and r is the distance the object is from the center of the earth.
a. solve the equation for r.
b. Suppose the object is 100 pounds when 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 to determine how much the object would weigh in Death Valley ( 282 feet below sea level) and The top of Mount Mc Kinley (20,320 feet above sea level)
I'm struggling with how to set these up. Any help?
a. To solve the equation w = Cr^(-2) for r, start by isolating r. Multiply both sides of the equation by r^2:
w * r^2 = C
Divide both sides of the equation by w:
r^2 = C / w
Finally, take the square root of both sides of the equation to solve for r:
r = sqrt(C / w)
b. Since the object weighs 100 pounds at sea level (w = 100) and the distance from the center of the earth at sea level is 3,963 miles (r = 3,963), we can substitute these values into the equation and solve for C:
100 = C * (3,963)^(-2)
Simplify the equation by squaring 3,963:
100 = C / (3,963 * 3,963)
Multiply both sides by (3,963 * 3,963) to solve for C:
C = 100 * (3,963 * 3,963)
Calculate the value of C using a calculator.
c. Now that we have found the value of C, we can use it to determine the weight of the object in Death Valley (282 feet below sea level) and the top of Mount McKinley (20,320 feet above sea level).
For Death Valley, the distance from the center of the Earth would be (3,963 - 0.282) miles. Substitute this value into the equation and calculate the weight.
For the top of Mount McKinley, the distance from the center of the Earth would be (3,963 + 20.32) miles. Substitute this value into the equation and calculate the weight.
Remember to convert units if necessary to ensure all calculations are in the same unit.