# 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?

Mar 26, 2016

5 pounds

#### Explanation:

The inverse relationship means that

${W}_{1} / {W}_{2} = {r}_{2}^{2} / {r}_{1}^{2}$

or

${W}_{1} {r}_{1}^{2} = {W}_{2} {r}_{2}^{2} = \text{constant}$

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

• ${r}_{1} = 5000 \text{mile}$
• ${W}_{1} = 20 \text{pound}$
• ${r}_{2} = 10000 \text{mile}$

We want to find ${W}_{2}$.

${W}_{1} / {W}_{2} = {r}_{2}^{2} / {r}_{1}^{2}$

${\left(20 \text{pound")/W_2 = (10000 "mile")^2/(5000 "mile}\right)}^{2}$

$= 4$

${W}_{2} = \frac{20 \text{pound}}{4}$

$= 5 \text{pound}$