Can a Waterfall Ever Become Supersonic?

[spacethisride]

Homework Statement

According to geologists, the water in a waterfall was supersonic, that is, it fell with speeds in excess of the speed of sound. Ignoring air resistance, what is the minimum height necessary to create a supersonic waterfall? (The speed of sound may be taken to be 340 m/s.)

Homework Equations

Treating water as particles, water falling down the fall is acted upon by gravity. Using the Newton's equation...I think??

S = ut + 1/2 at^2

The Attempt at a Solution

S = ut + 1/2 at^2

h = 340t + (9.8/2)t^2
4.9t^2 +340t - h = 0. Solve the quadratic equation for t?

But I have two variables...(h and t) so I don't know how to go any further...

 

[Integral]

you need to use the veloctiy relationship

$$v = v_0 + gt$$

to find the time required to reach 340 m/s then use that time in the distance relationship to find the distance.