Could someone please check my work on these word problems? My solutions just don't seem right, could you please let me know where I may have messed up.
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.
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 Death Valley (282 feet below sea level) 282ft=0.053409mi??
My solutions:
a. r=sqrt(C/w)
b. w=Cr^-2 or w=C*1/(r^2) ??
100=C(1/3,963^2)
100=C(1/15,705,369)
100*15,705,369=C(1/15,705,369)*15,705,369
C=1,570,536,900 ??
c. w=1,570,536,900(1/0.053409^2)
w=1,570,536,900(1/0.002853)
w=1,570,536,900(350.508237)
???? w=550,486,119,962.4453 ??
If you could let me know if and where I may have made any mistakes I'm sure I could complete the rest of the assignment.
Thank you!