A body’s weight varies inversely with the square of its distance from the center of the earth; if a chicken weighs 20 pounds when it is 5000 miles from the earth’s center, how much will the chicken weigh when it is 10000 miles from the earth’s center?

1 Answer
Mar 26, 2016

Answer:

5 pounds

Explanation:

The inverse relationship means that

#W_1/W_2 = r_2^2/r_1^2#

or

#W_1 r_1^2 = W_2 r_2^2 = "constant"#

where #W_1# is the weight when the distance is #r_1#, and #W_2# is the weight when the distance is #r_2#.

Now, we know that

  • #r_1 = 5000 "mile"#
  • #W_1 = 20 "pound"#
  • #r_2 = 10000 "mile"#

We want to find #W_2#.

#W_1/W_2 = r_2^2/r_1^2#

#(20 "pound")/W_2 = (10000 "mile")^2/(5000 "mile")^2#

#= 4#

#W_2 = (20 "pound")/4#

#= 5 "pound"#