Can a Waterfall Ever Become Supersonic?

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AI Thread Summary
The discussion centers on calculating the minimum height required for water in a waterfall to achieve supersonic speeds, defined as exceeding 340 m/s. The approach involves using kinematic equations, specifically S = ut + 1/2 at^2, to relate height, time, and acceleration due to gravity. The user attempts to set up a quadratic equation but struggles with having two variables, height (h) and time (t). They are advised to first determine the time needed to reach the supersonic speed using the velocity relationship v = v_0 + gt, and then substitute this time back into the distance equation to find the necessary height. The discussion highlights the complexity of the problem and the need for a systematic approach to solve it.
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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...
 
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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.
 

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