{Use of Tech} A pursuit curve A man stands 1 mi east of a crossroads. At noon, a dog starts walking north from the crossroads at 1 mi/hr (see figure). At the same instant, the man starts walking and at all times walks directly toward the dog at s > 1 mi/hr . The path in the xy-plane followed by the man as he pursues the dog is given by the function y = ƒ(x) = s/2 ((x(ˢ⁺¹)/ˢ) /(s+1) - (x(ˢ⁺¹)/ˢ / s-1)) + s/ s² - 1


Select various values of s > 1 and graph this pursuit curve. Comment on the changes in the curve as s increases. <IMAGE>

Verified step by step guidance

1. Understand the problem: We have a man and a dog starting at different points and moving in such a way that the man's path is described by a pursuit curve. The man's speed is greater than 1 mi/hr, and we need to analyze how this speed affects the path he takes.
2. Identify the function: The path of the man is given by the function y = f(x) = \frac{s}{2} \left( \frac{x^{(s+1)/s}}{s+1} - \frac{x^{(s+1)/s}}{s-1} \right) + \frac{s}{s^2 - 1}. This function describes the y-coordinate of the man's position as a function of his x-coordinate.
3. Select values of s: Choose various values of s greater than 1, such as s = 1.5, s = 2, s = 3, etc. These values will help us understand how the man's speed affects the shape of the pursuit curve.
4. Graph the pursuit curve: For each selected value of s, plot the function y = f(x) on a graph. This will visually show how the path changes as the man's speed changes.
5. Analyze the changes: Observe the graphs for different values of s. As s increases, note how the curve becomes steeper or changes direction. Comment on these changes, focusing on how the man's increased speed affects his ability to catch up to the dog.