Question

A long straight river, 100 meters wide, is flowing at 1 meter per second. A pollutant is entering the river at a constant rate from one of its banks. As the pollutant disperses in the water, it forms a plume that is modeled by the equation y=√x . Use this information to answer the following questions.
a. How wide is the plume 484 meters down river from the source of the pollution? meters
b. How wide is the plume 441 meters down river from the source of the pollution? meters
c. How far down the river from the source of the pollution does the plume reach halfway across the river? meters
d. How far down the river from the source of the pollution does the plume reach the other side of the river? meters

Answer 1

Answer with Step-by-step explanation:

We are given that

Width of river=100 m

Rate of flowing=1 m/s

The equation of plum is given  by

$y=\sqrt x$

a.x=484 m

$y=\sqrt{484}=22 m$

Width of plum=22 m

b.x=441 m

$y=\sqrt{441}=21 m$

c.When the plume reach halfway across the river

Then, width of plume=$y=\frac{1}{2}(100)=50 m$

$50=\sqrt x$

Squaring on both sides

$x=(50)^2=2500 m$

d.y=100 m

$100=\sqrt x$

Squaring on both sides

$x=(100)^2=10000 m$