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.

 

[Moetasim]

I would like to clarify that the concept of a supersonic waterfall is not supported by current scientific understanding. The speed of sound is determined by the medium through which it travels, and in the case of water, it is significantly lower than the speed of sound in air. Therefore, it is not possible for water to fall at supersonic speeds.

Additionally, the equation you have used is incorrect for this scenario. The equation S = ut + 1/2 at^2 is applicable for an object falling under the influence of gravity, but it does not take into account the drag force caused by air resistance. In reality, the maximum speed a falling object can reach is known as the terminal velocity, which is determined by the balance between the force of gravity and the drag force.

In summary, the concept of a supersonic waterfall is not supported by scientific evidence and the approach used in the attempted solution is not applicable.