Download Appendix: 1. Many people know that the weight of an object varies

Appendix:
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 the earth.
a. Solve the equation for r.
W = C/r^2
Multiply by r^2:
Wr^2 = C
divide by W:
r^2 = C/W
Square root:
r = sqrt(C/W)
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.)
Use the first equation:
100 = C/3963^2
Multiply by 3963^2:
100*3963^2 = C
C = 1570536900
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)
w = C/r^2
r = 3963 - 282/5280
w = 1570536900/(3963 - 282/5280)^2
w = 100.002695 pounds
ii. The top of Mt McKinley (20,320 feet above sea level)
r = 3963 + 20320/5280
w = 1570536900/(3963 + 20320/5280)^2
w = 99.806 pounds
2. The equation gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
Confirm that the equation is:
D = 1.2*sqrt(h)
a. Solve this equation for h.
Divide by 1.2:
sqrt(h) = D/1.2
Square:
h = (D/1.2)^2
Long's Peak in the 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)? Explain your answer
D = 1.2*sqrt(14255)
D = 143.273 miles
Yes, you can see Cheyenne, since this number is much greater than 89 miles.
MAT 117
Number 1:
80
Number 2:
21
Number 3 seemed the same as 2
Number 4:
5 |x|
Number 5:
(xy^5z)^1/6
Number 6:
y
Number 7:
-1
Number 8:
3
Number 9:
6^21/50
MAT 117
Number 10:
2√5
Number 11:
Exact = √74
Approx = 8.602
Number 12:
3
Number 13:
21
Number 14:
13 + 7√2
Number 15:
Choice D
Number 16:
-10
Number 17:
27
Number 18:
MAT 117
Number 19:
Number 20:
9a^7b^3 √6ab
Number 21:
16√y
MAT 117
Number 22:
47/3
Number 23:
3
Number 24:
-27 + 8√3
MAT 117