Chapter 7.1, Problem 33E

To determine

To Find:Distance of each animal from the fulcrum? Justify.

Answer to Problem 33E

The distance of the cat from fulcrum is $4ft$ and that of dog is $2ft$

Explanation of Solution

Given:To balance the board in the diagram, the distance (in feet) of each animal from the center of the board must vary inversely with its weight (in pounds).

  

Distance varies inversely with weight

i.e.

  $d=\frac{a}{w}$

Since the distance varies inversely with weight

Therefore the product must be constant

  $d\times w=a$

i.e.

Let $d_1$ represents the distance of the cat from fulcrum and $d_2$ be of the dog.

Then

  $\begin{array}{l}{d}_1\times w_1=d_2\times w_2\\ d_1\times 7=d_2\times 14\\ 7d_1=(6-d_1)\times 14\\ 7d_1=84-14d_1\\ 21d_1=84\\ d_1=4\\ d_2=6-d_1\\ d_2=6-4\\ d_2=2\end{array}$

Hence, the distance of the cat from fulcrum is $4ft$ and that of dog is $2ft$