Question

The mass of the particles that a river can transport is proportional to the fifth power of the speed of the river. A certain river normally flows at a speed of 3 miles per hour. What must its speed be in order to transport particles that are 16 times as massive as usual

Answer 1

Answer: V = 5.22m/s

Explanation:

Given that the mass of the particles is proportional to the fifth power of the speed. That is

M = k V^5

Where M = mass and V = speed

K = constant of proportionality

A certain river normally flows at a speed of 3 miles per hour

V = 3 mph

M = unknown

M = k × 3^5

M = 243K

K = M/243 ........(1)

What must its speed be in order to transport particles that are 16 times as massive as usual

M = 16M

Using same formula

I.e M = KV^5

16M = M/243 × V^5

M will cancel out

16 = V^5/243

V^5 = 3888

V = 5.22m/s