You are playing disc golf, and you throw your frisbee at the basket. It's soaring high through the air, flying beautifully toward the chains, and then it hits the top of a thick pine tree (oh no!). As it falls from the top of the tree, it hits a single branch, and then continues to fall.

If the time it takes for the frisbee to fall freely from the top of the tree is \(t_\textrm{top}\), find \(t_\textrm{max}/t_\textrm{top}\), where \(t_\textrm{max}\) is the greatest amount of time the frisbee can take to fall to the ground.

**Assumptions**

- The frisbee falls like a point particle.
- The frisbee instantly comes to a stop when it hits the branch, then continues to fall.
- The branch can be located anywhere from the ground to the top of the tree.

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