Hint: 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: , where C is a constant, and r is the distance that the object is from the center of 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 Mount McKinley (20,320 feet above sea level).
What is the equation?
To solve the equation for r, we need to isolate r on one side of the equation. The equation is given as:
Weight = C/r
a. To solve for r, we can rearrange the equation as:
r = C/Weight
b. To find the value of C, we can substitute the values given into the equation and solve for C. We know that Weight = 100 pounds and the distance from the center of the Earth at sea level is 3,963 miles.
Using the equation:
100 = C/3,963
To solve for C, multiply both sides of the equation by 3,963:
C = 100 * 3,963
You can use a calculator to find the value of C.
c. Now that we have the value of C, we can use it to determine the weight of the object in different locations.
i. To find the weight in Death Valley (282 feet below sea level), we need to calculate the distance from the center of the Earth to Death Valley in miles. We can convert the given distance from feet to miles using the conversion factor 1 mile = 5,280 feet:
Distance to Death Valley = 282 feet / 5,280 feet/mile
Calculate the distance to Death Valley in miles.
Now, using the value of C and the distance to Death Valley, we can calculate the weight using the equation:
Weight = C / Distance to Death Valley
ii. To find the weight at the top of Mount McKinley (20,320 feet above sea level), we need to calculate the distance from the center of the Earth to the top of Mount McKinley in miles. Follow the same process as in part i to convert the given distance to miles.
Now, using the value of C and the distance to the top of Mount McKinley, we can calculate the weight using the equation:
Weight = C / Distance to top of Mount McKinley
By substituting the values into the equation and calculating, you can determine the weight in Death Valley and at the top of Mount McKinley.