Is there anything in the rules that says that we can or cannot use a fiberglass fishing rod as a throwing arm on our robot.
As long as it’s not unsafe, and it costs less than $400 then yes.
If you want to build a spring powered catapult you might want to consider a section of a cross country ski, or toy bow and arrow as sources of material. Both can usually be found cheaply at many goodwill stores. We prototyped such a launcher and it can be made extremely accurate and reasonably powerful. Our students really want to do a reaction wheel, but I think that is more weight and complexity than required. Take a look at the soccer kicker that the robowranglers did a few years back for ideas. They used a simple cam to control the spring.
Of course it must fit inside the size and weight constraints and be listed on your BOM at cost. However, since fiberglass has a tendency to fracture, you may be called for having an unsafe mechanism.
I saw a couple of teams try that approach in “Breakaway”, using a V-shaped apparatus to try and launch a hanging hook onto the tower. Many found that they had significant control issues when they released the poles, since they would tend to twist when they were released. I would guess the size and weight of a basketball would magnify that issue.
What we’ve used before was some thin diameter (I can’t remember the exact measurement) PVC tubing. We did that in 2010 in an attempt to fling a hook up to the bar to hang. It’d be pretty cheap, and if you’re looking to rapidly prototype, then it’d be convenient until you find a better material.