Chapter 5.2, Problem 56E

To determine

(a)

To find:

The value of $s\left(\frac{\pi }{2}\right)$ where the distance $s$ of a piston with respect to angle $\theta$ of the connecting rod as indicated in the figure is given by the formula

$s\left(\theta \right)=2.625\cos \theta +2.625{\left(15+{\cos }^2\theta \right)}^{1/2}$

where $s$ is measure in inches and $\theta$ in radians.

To determine

(b)

To find:

The $\frac{ds}{d\theta }$ when $s\left(\theta \right)=2.625\cos \theta +2.625{\left(15+{\cos }^2\theta \right)}^{1/2}$.

To determine

(c)

To find:

The values of $\theta$ where the maximum velocity of the piston occurs.