Today we find out.
We have two knowns. Distance and acceleration. Like any sensible person I will convert everything to the metric system, duh. The metric system is sweet.
distance=186 feet= 56.6928 meters
acceleration= gravity= 9.831 m/s^2 (meters per second squared)
Then we start with what we know.
Velocity is equal to acceleration times time.
v = a t
Acceleration in this case is gravity so
v = gt
Then you integrate with respect to time and get
c is a constant that tells us the starting point of his falls, we will set it to zero. c=0
then we substitute the known values
solving for t we get
The we put it back into our original equation to determine his velocity upon entering the water
which translates to
That is really fast! Much faster than I would ever like to go in a kayak.
Is this the limit?
This section is highly speculative and not meant as an endorsement for running waterfalls of any height, let alone those above 186 ft.
Two percent of people survive the 245 ft leap from the Golden Gate. This is a leap into completely green water, there is no aeration to soften the impact. Now saying that there is a 2% survival rate is not a strong argument for running a waterfall that is that tall, but it goes to show that it is possible to survive a fall of 245 feet into water. There are certainly other problems with the idea. First of all, it will be difficult to find a waterfall that is that tall that shares all the characteristics of Palouse: The big pool, the minimal risk of going behind the falls, the relatively flat entrance, and big flows all contributed to its appeal. All this aside it is possible to survive, and if the possibility alone doesn't inspire you, I just don't know what else will.