The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river.

Question

The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain river normally flows at a speed of 2 miles per hour. What must its speed be in order to transport particles that are 15 times as massive as usual?

Answer 1

You can set this up for solution as a proportion.

 

m = mass that gets transported at 2 mph

v = speed needed to transport 15m

 

m/2⁶ = 15m/v⁶ ⇒

 

1/2⁶ = 15/v⁶

 

v⁶ = 15(2⁶)

 

v = 2(15^1/6) mph

Answer 2

Heavier mass will move slower so the relation must be an inverse one. To move heavier mass will require a higher speed.

Let the mass of the particles at normal flow be x which corresponds to speed 2miles/hr

m is proportional to 2^6= 64/hr

15m will require a speed proportional to 64*15 =960

The River then would need to move at a speed of 2Xsixth root of 15 miles/hr Speed=3.14 miles/hr