Chapter 9.5, Problem 11PPS

To determine

To write an equation that relates weight on the moon $\frac{1}{6}w$ with weight on earth $\left(w\right)$ .

Answer to Problem 11PPS

the variation equation $m$ is $\frac{1}{6}w$

Explanation of Solution

Given information:

The weight on the moon is directly proportional to the weight on the earth.

Weighted $360$ pounds on earth with all his equipment on.

But weighted $60$ pounds on moon.

Calculation:

The equation that relates weight on the moon $\left(m\right)$ with weight on earth $\left(w\right)$ is .

First set up the correct proportion for the given information.

  $\begin{array}{l}m\propto w\left[\sin ce,m=\text{moon,}w=\text{earth}\right]\\ m=kw\left[k=\text{constant}\right]\\ k=\frac{m}{w}\left[\text{direct variation}\right]\end{array}$

Put the values of $w=360$ , $m=60$ in above equation

  $\begin{array}{l}k=\frac{60}{360}\\ k=\frac{60}{360}\\ k=\frac{1}{6}\left[\text{divide numerator and denominator by 60}\right]\end{array}$

Hence,

the variation equation $m$ is $\frac{1}{6}w$