Answer
$2m$: $v=1.122\text{ m/s}$
$10m$: $v=1.468\text{ m/s}$
$100m$: $v=2.154\text{ m/s}$
Work Step by Step
Let's note:
$m$ = the mass of particles
$v$ = the speed of the river
$k$ = the constant of variation.
Because the mass of particles is proportional to the sixth power of the river's speed, we can write the variation equation:
$$\begin{align}m=kv^6.\end{align}\tag1$$
Substitute $v=1$ in equation $(1)$:
$$m=k(1^6)\Rightarrow \dfrac{m}{k}=1.\tag2$$
For a mass $2m$ equation $(1)$ becomes (using equation $(2)$ too):
$$2m=kv^6\Rightarrow v^6=\dfrac{2m}{k}\Rightarrow v^6=2$$
Solve for $v$:
$$v=\sqrt[6]2\approx 1.122\text{ meters per second}.$$
For a mass $10m$ equation $(1)$ becomes (using equation $(2)$ too):
$$10m=kv^6\Rightarrow v^6=\dfrac{10m}{k}\Rightarrow v^6=10$$
Solve for $v$:
$$v=\sqrt[6]{10}\approx 1.468\text{ meters per second}.$$
For a mass $100m$ equation $(1)$ becomes (using equation $(2)$ too):
$$100m=kv^6\Rightarrow v^6=\dfrac{100m}{k}\Rightarrow v^6=100$$
Solve for $v$:
$$v=\sqrt[6]{100}\approx 2.154\text{ meters per second}.$$
