Chapter 9.4, Problem 17Q

Solution

To find: The distance above the ground of the stuntman at the beginning and at the end of the swing.

  $18.762\text{feet}$ approximately.

Given information:

A stuntman uses a $30$ feet rope to swing ${136}^{\circ }$ between two platforms of equal height, grazing the ground in the middle of the swing. If the rope stays taut throughout the swing, how far above the ground was the stuntman at the beginning and the end of the swing. How far apart are the platform.

Explanation:

The length $\left(L\right)$ of the rope is

  $30$ feet and $\theta ={136}^{\circ }$ .

Let $h$ be the height of the stuntman above the ground.

Use the trigonometric identity to find the height of the stuntman above the ground:

  $\begin{array}{l}h=L(1-\cos 0.5\theta )\\ =30\left(1-\cos \left(0.5\times {136}^{\circ }\right)\right)\\ =30\left(1-\cos {68}^{\circ }\right)\\ =30\left(1-0.3746\right)\\ \approx 30\times 0.6254\\ \approx 18.762\end{array}$

Hence, the stuntman at the beginning and at the end of the swing was approximately $18.762\text{feet}$ above the ground.