Answer:
6.58 miles per hour
Step-by-step explanation:
Let the mass and speed be represented by m and s respectively. So that,
m [tex]\alpha[/tex] [tex]s^{5}[/tex]
m = k[tex]s^{5}[/tex]
where k is the constant of proportionality.
For a certain river, speed = 4 miles per hour.
m = k [tex](4)^{5}[/tex]
m = 1024k ............ 1
In order to transport particles that are 12 times as massive as usual;
12m = k[tex]s^{5}[/tex]
m = [tex]\frac{ks^{5} }{12}[/tex] ............. 2
Thus,
[tex]\frac{ks^{5} }{12}[/tex] = 1024 k
[tex]s^{5}[/tex] = 12 x 1024
= 12288
[tex]s^{5}[/tex] 12288
s = [tex]\sqrt[5]{12288}[/tex]
= 6.5750
s = 6.58 miles per hour
Therefore, its speed must be approximately 6.58 miles per hour.
