Since this wooden rod travels several miles in a 6 second time frame - traveling more than 500M/s on average - don't we have to assume it accumulates?
Falling damage is the mechanism that makes the most sense to shoehorn in there. Using an improvised weapon on a rod already traveling more than 500M/s seems even more clumsy, as well as calculating the damage more wibbly-wobbly.
There's also the rule of cool. If it makes the story better/ more enjoyable: have at it.