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

Answer:

$v_2 \approx 1.12246\ m.s^{-1}$

$v_{10}\approx 1.4678\ m.s^{-1}$

$v_{100}\approx 1.4678\ m.s^{-1}$

Step-by-step 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:

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

$v_{100}\approx 1.4678\ m.s^{-1}$