Answer the following questions using an Equation Editor to write mathematical expressions and equations.
Hint for this assignment: Pay attention to the units of measure. You will have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions.
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 w is weight in pounds
r is the distance in miles from the center of the earth
C is a constant with units
1. Solve the equation for r; use rules for exponents, roots, and square roots.
2 Solve the equation for C; use rules for exponents, roots, and square roots.
3. 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.)
4. Use the value of C you found in the previous question to determine how much the 100 pound object would weigh at different distances from the center of the earthUse the equation
a. Dead Sea which is 1369 feet below sea level
First convert feet to miles and calculate the distance from the center if the earth
b. Use this radius to determine how much the 100 object would weigh at the Dead Sea.
c. The top of Mt Everest at 29035 feet above sea level
First convert feet to miles and calculate the distance from the center if the earth
d. Use this radius to determine how much the 100 object would weigh on the top of Mt Everest.
5. Solve this equation for h; include units as a check
6. Long's Peak in the Rocky Mountain National Park, is 14,255 feet in elevation above sea level and the Colorado Plains are 4800 feet above sea level.
a. First calculate the height of Longs Peak above the Plains
b. Then calculate how far can you see toward the horizon across the plains from the top of Long's Peak?
7. From the Top of Longs Peak can you see Cheyenne Wyoming 89 miles away and 6063 feet above sea level?
a. First calculate the height of Longs Peak above the Cheyenne
b. Then calculate how far can you see from the top of Long's Peak toward Cheyenne