Question 513835: 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 gravitational constant with units
Note: units are included for consistency
1. Solve the equation for r; use algebraic rules for exponents, roots, and square roots.
2 Solve the equation for C(gravitational constant); use algebraic rules for exponents, roots, and square roots.
3. Suppose that an object is 150 pounds when it is at sea level. Find the value of gravitational constant C150, for 150 pounds, which makes the equation true.
(Sea level is 3,963 miles from the center of the earth.)
4. Use the value of C150 for 150 pounds you found in the previous question to determine how much the 150 pound object would weigh at a different distance from the center of the earth
a. The lowest natural point on Earth is at the bottom of the Mariana Trench 35,797 feet below sea level
First convert feet below sea level to miles and then calculate the distance of the bottom of the trench from the center of the earth
b. Use this radius from the center of the earth and the value of C150 for 150 pounds from the previous question, to determine how much the 150 object would weigh in the Mariana Trench
Use the equation
5. Suppose that an object is 175 pounds when it is at sea level. Find the value of gravitational constant C175, for 175 pounds, which makes the equation true.
(Sea level is 3,963 miles from the center of the earth.)
a.
b. The summit of the Volcano Chimborazo in central Ecuador, is 3,967 miles from the Center of the earth. Use this radius and the value of C175 for 175 pounds from the previous question. to determine how much the 175 object would weigh on the summit.
Use the equation
The equation below gives the distance that a person can see to the horizon from Height
Where D, is distance, in miles
h, in height feet
Note: units are included for consistency
6. Solve this equation for h; include units as a check
7. Long’s Peak in the Rocky Mountain National Park, is 14,255 feet in elevation above sea level and Fort Morgan Colorado is 4324 feet above sea level.
a. First calculate the height in feet of Longs Peak above the Fort Morgan
b. Using this height can you see Fort Morgan 103 miles from the Top of Longs Peak?
8. Piles Peak in Colorado is 14,115 feet in elevation above sea level and Arriba Colorado is 5239 feet above sea level.
a. First calculate the height in feet of Pikes Peak above the Arriba
b. From the Top of Piles Peak can you see Arriba 117 miles away?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
This question, or one very much like it, has been answered several times on this site. I've even answered it a couple of times. Spend a little time searching.
John
My calculator said it, I believe it, that settles it
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