Question

A trout jumps, producing waves on the surface of a 0.8-mdeep mountain stream. If it is observed that the waves do not travel upstream, what is the minimum velocity of the current?

Answer 1

Answer:

The value is $v = 2.8 \ m/s$

Explanation:

From the question we are told that  

     The depth of the mountain is  $d = 0.8 \ m$

Generally the  velocity of the surface  wave  is mathematically represented as

        $v = \sqrt{ g * d }$      

=>      $v = \sqrt{ 9.8 * 0.8 }$    

=>      $v = 2.8 \ m/s$

Generally using the Froude number is mathematically represented as

          $Fr = \frac{ V }{ v }$

Here V is the velocity of the current

 Given that  the waves do not travel upstream, then the flow of the current is  supercritical which means that

            $\frac{ V }{ v } > 1$

=>         $V > v$

=>         $V > 2.8 \ m/s$

Hence the minimum velocity of the current  is  

            $v = 2.8 \ m/s$

This because the velocity of the  current is greater velocity of the surface  wave , so minimum will be like the lowest possible value of  V  which is v