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 1 meter per second. What must its speed be in order to transport particles that are twice as massive as usual? 10 times as massive? 100 times as massive?

Answer 1

`v_2 \approx 1.12246\ m.s^(-1)`

`v_(10)\approx 1.4678\ m.s^(-1)`

`v_(100)\approx 1.4678\ m.s^(-1)`

Explanation:

Mass of particles that a river can transport,
`m\propto\ v^6`

where:

v = velocity of river flow

When
`v=1\ m.s`

then the mass transported,
`m \propto 1^6`

When mass is twice:

`v=\sqrt[6]{2}`

`v_2 \approx 1.12246\ m.s^(-1)`

When mass is 10 times:

`v=\sqrt[6]{10}`

`v_(10)\approx 1.4678\ m.s^(-1)`

When mass is 100 times:

`v=\sqrt[6]{100}`

`v_(100)\approx 1.4678\ m.s^(-1)`