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.

Question

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 w=Cr^-2 for r. The answer I came up with is r^-2=w/C: is this correct?
And would you please help me with b?
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.)
Thank you!

Answer 1

Ok, I went back and tried again. The equation I found when solving for r is r=sqrt(C/w)

Is this correct?
Then in b I would plug in the 100 for w, and the 3,963 for r to find the constant, C, correct?

Answer 2

a is correct.

C = w/r^-2

w = 100

r = 1/(3963)^2

Solve for C.

Answer 3

So would my equation be C=100/(3963)^2 ...I'm confused

Answer 4

Please let me know if I did this correct for b...

100=C/(3,963)^2
100=C/15,705,369
100*C=(C/15,705,369)*C
100C=15,705,369
100C/100=15,705,369/100
C=157,053.69

Answer 5

a. To solve the equation w = Cr^(-2) for r, we can start by rearranging the equation.

First, divide both sides of the equation by C to isolate the r term:

w/C = r^(-2)

Next, to eliminate the negative exponent, we take the reciprocal of both sides of the equation:

(C/w) = r^2

Now, take the square root of both sides to solve for r:

r = √(C/w)

So, the correct answer is r = √(C/w).

b. In this case, we are given that the weight of an object at sea level is 100 pounds, and the distance from the center of the Earth at sea level is 3,963 miles.

Using the equation w = Cr^(-2), we substitute the known values into the equation:

100 = C(3963)^(-2)

Now, we can solve for C:

C = (100) / (3963)^(-2)

To evaluate this, we need to calculate (3963)^(-2). Taking the reciprocal of the square of 3963, we get:

C ≈ (100) / (0.00000006312)

Simplifying,

C ≈ 1,584,375,000

Therefore, the value of C that makes the equation true in this case is approximately 1,584,375,000.