Chapter 9.2, Problem 48WE

To determine

To find: The path followed by the midpoint of the ladder during slippage.

Answer to Problem 48WE

The path followed by the midpoint of the ladder is part of a circle, having a center at $\left(0,0\right)$ and radius of $3m$ .

Explanation of Solution

Given information: The length of the ladder is 6m long.

Formula used: $d=\frac{r}{2}$

Calculation: Since the total length of the ladder is 6m that means the diameter is 6m. And when the ladder falls completely on the ground, the midpoint of the ladder is going to be aligned with it. Hence,

  $\begin{array}{l}r=\frac{6}{2}\\ r=3m\end{array}$

By observing the given picture, we can say that the midpoint of the ladder is part of a circle that is centered at the origin. Hence,

  $\left(h,k\right)=\left(0,0\right)$

Therefore, the path followed by the midpoint of the ladder is part of a circle, having a center at $\left(0,0\right)$ and radius of $3m$ .