To determine how long it takes for the ball to go through the hoop, we need to find the point of intersection of the two paths: the path of the ball \( b(s) \) and the path of the hoop \( h(s) \).
However, since I can't see the graph or the specific equations for \( b(s) \) and \( h(s) \), I can't calculate the exact time it takes for the ball to pass through the hoop.
If you've already solved for the intersection or have the equations, you can substitute the time values back into the equations to find when the ball and the hoop are at the same point in space. The x-coordinates (time) where they intersect will give the answer.
If you have the numerical values/result from your calculations or any additional information about the specific equations or graphical representation, please share, and I can help you reason through it! Otherwise, choose the response that you believe is correct based on your understanding or calculations.