To determine how long it takes for the ball to go through the hoop, we would typically need to analyze the paths represented by \( b(s) \) for the ball and \( h(s) \) for the hoop. Since I don't have access to the specific curves or any additional information about their equations or the positions of the ball and the hoop at various times, I'm unable to calculate the time directly.
However, if this is a question from a specific problem or scenario you have in front of you, you should look for intersections or points where the ball's path meets the hoop's path. The intersection points can help deduce how long it takes for the ball to enter the hoop.
If you provide more context, data, or details about the curves, I might be able to help you better. Otherwise, based solely on the options you've listed, it's impossible for me to determine the correct answer without further information.
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