Using the formula: w=Cr^-2 where C is a constant, and r is the distance that the object is from the center of Earth. W is the weight.
1- Suppose an object is 100lbs 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.
sub in the given data ...
100 = C(3963)^-2
C = 100(3963)^2 ... huge number
Would you not divide the big number by 100 to get C alone?
100 = C(3963)^-2
100 = C/3963^2 , so now we have to mutiply both sides by 3963^2 to get C alone, like I had
To find the value of C that makes the equation true, we need to substitute the given values into the formula and solve for C.
We are given that the weight of the object when it is at sea level (r = 3,963 miles) is 100 lbs. So, we have:
w = 100 lbs
r = 3,963 miles
The formula is w = C * r^(-2).
Substituting the given values into the formula, we have:
100 lbs = C * (3,963 miles)^(-2)
Now, let's simplify it step by step. First, we can rewrite (3,963 miles)^(-2) as 1 / (3,963 miles)^2:
100 lbs = C * 1 / (3,963 miles)^2
Next, we calculate (3,963 miles)^2:
100 lbs = C * 1 / 15,702,369 miles^2
Now, we can simplify it further by taking the reciprocal of both sides:
1 / 100 lbs = C / 15,702,369 miles^2
To isolate C, we multiply both sides by 15,702,369 miles^2:
C = (1 / 100 lbs) * 15,702,369 miles^2
Finally, we can calculate the value of C:
C ≈ 157,023.69 lb * miles^2
Therefore, the value of C that makes the equation true is approximately 157,023.69 lb * miles^2.