Expert: Richard J. Raridon - 2/22/2010

Question
I have a few questions that I am having a hard time grasping the concepts:
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: 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  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).

2.   The equation d=1.2 square root of h, gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.

a.   Solve this equation for h.  

b.   Long’s Peak in Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)?
Thanks

Answer
I have taught physics and am well aware that weight varies slightly over the face of the Earth.
1. a. r = (C/W)^1/2
b. C = Wr^2 = 100(3963)^2 = 1570536900, ordinarily, you would just write that as 1.570x10^9 but then you couldn't do c.
c. i. r = 3963-0.0534 so W = 100.0027 lb.
ii. r = 3963+3.8485 so W = 99.806 lb.
2. a. h = d^2/1.44
b. d = 1.2(14255)^1/2 = 143.3 miles, yes