Chapter 11, Problem 13PS

Tetherball A tetherball weighing 1 pound is pulled outward from the pole by a horizontal force u until the rope makes an angle of $\theta$ degrees with the pole (see figure).

(a) Determine the resulting tension in the rope and the magnitude of u when $\theta ={30}^{\circ }$.

(b) Write the tension T in the rope and the magnitude of u as functions of $\theta$. Determine the domains of the functions.

(c) Use a graphing utility to complete the table.

$\theta$	0°	10°	20°	30°	40°	50°	60°
T
$\Vert u\Vert$

(d) Use a graphing utility to graph the two functions for $0^{\circ }\le \theta \le {60}^{\circ }$.

(e) Compare T and $\Vert u\Vert$ as $\theta$ increases.

(f) Find (if possible)

$\underset{\theta \to \pi /2^{-}}{\lim }T\text{and}\underset{\theta \to \pi /2^{+}}{\lim }\Vert u\Vert$

Are the results what you expected? Explain.