# A Supersonic Waterfall?

1. Jul 6, 2008

### spacethisride

1. The problem statement, all variables and given/known data
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.)

2. Relevant 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

3. 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...

2. Jul 6, 2008

### Integral

Staff Emeritus
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.