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

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

Step-by-step 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 = √( g * d )`

=>
`v = √( 9.8 * 0.8 )`

=>
`v = 2.8 \ m/s`

Generally using the Froude number is mathematically represented as

`Fr = ( 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

`( 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