Chapter 10.5, Problem 6STP

An amusement park ride is a spinning cylinder. At a certain speed the riders are pinned against the walls by the force of the spin and the floor drops out safely. The speed s in meters per second that is needed to pin the riders is given by s - 4,95 Vr where r is the radius of the cylinder in meters.

1. Graph the function.
2. What is an estimate for the radius of the ride if s — 12 meters per second? Round to the nearest hundredth of a meter.

To determine

To graph: the function.

Explanation of Solution

Given information:

The function is $s=4.95\sqrt{r}$ .

Graph: to draw the graph, use the point plotting method,

$r$	$s$
$4$	$8.90$
$1$	$4.95$
$2$	$4.95\sqrt{2}$

Now, by using the above table, the graph can be obtained as:

  

Interpretation: from the above table it can be observed that the domain of the function is $r\ge 0$ .

To determine

To find: the radius.

Answer to Problem 6STP

The radius is $r=5.85$ .

Explanation of Solution

Given information:

The function is $s=4.95\sqrt{r}$ .

Calculation: to find the radius first substitute and then simplify,

  $\begin{array}{l}s=4.95\sqrt{r}\\ 12=4.95\sqrt{r}\text{ [substitute]}\\ \sqrt{r}=2.42\text{ [divide]}\\ r=5.85\text{ [square]}\end{array}$

Thus, the radius is $r=5.85$ .