Chapter 8.2, Problem 41E

a.

To determine

To solve:

The given equation for s to obtain an equation that gives speed as a function of stride frequency.

Answer to Problem 41E

The equation $s=\frac{f-1.19}{2.13}$ gives speed as a function of stride frequency.

Explanation of Solution

Given:

The Platypus is an animal with a broad flat tail, webbed feet, and a snout like duck’s bill. Although a platypus spends much of its time in water, it can also walk on land. The diagram, below shows one complete stride of a walking platypus. The stride frequency f is the number of strides per second the platypus takes. It can be approximated by the equation $f=2.13s+1.19$ , where s is the speed of platypus in meters per second.

  

Calculation:

We will solve our given equation for s using opposite operations as:

  $\begin{array}{l}f=2.13s+1.19\left(\text{Given equation}\right)\\ 2.13s+1.19=f\left(\text{Switching sides}\right)\\ 2.13s+1.19-1.19=f-1.19\left(\text{Subtracting }1.19\text{}\text{from both sides}\right)\\ 2.13s=f-1.19\\ \frac{2.13s}{2.13}=\frac{f-1.19}{2.13}\left(\text{Dividing both sides by 2}\text{.13}\right)\\ s=\frac{f-1.19}{2.13}\end{array}$

Therefore, the equation $s=\frac{f-1.19}{2.13}$ gives speed as a function of stride frequency.

b.

To determine

To approximate:

The speed of a platypus that takes 3 strides per second. Round your answer to the nearest tenth of a meter per second.

Answer to Problem 41E

The speed of the platypus would be approximately 0.8meters per second.

Explanation of Solution

Given:

The Platypus is an animal with a broad flat tail, webbed feet, and a snout like duck’s bill. Although a platypus spends much of its time in water, it can also walk on land. The diagram, below shows one complete stride of a walking platypus. The stride frequency f is the number of strides per second the platypus takes. It can be approximated by the equation $f=2.13s+1.19$ , where s is the speed of platypus in meters per second.

  

Calculation:

To find the speed of the platypus, we will substitute $f=3$ in our given equationas:

  $\begin{array}{l}s=\frac{f-1.19}{2.13}\left(\text{Given equation}\right)\\ s=\frac{3-1.19}{2.13}\left(\text{Substituting }f=3\right)\\ s=\frac{1.81}{2.13}\\ s=0.849765258\\ s\approx 0.8\left(\text{Rounding to nearest tenth}\right)\end{array}$

Therefore, the speed of the platypus would be approximately 0.8 meters per second.