Question

The speed of the water in a whirlpoil varies inversely with the radius. if the water speed is 2.5 feet per second at a radius of 30 feet what js the speed of the water at a radius of 3 feet?​

Answer 1

Answer:

25 feet per second.

Step-by-step explanation:

Let s represent the speed of the water and r represent the radius of the whirlpool.

The speed in a whirlpool varies inversely with the radius. Therefore, we can write that:

$\displaystyle s=\frac{k}{r}$

Where k is the constant of variation.

We know that the speed is 2.5 feet per second when the radius is 30 feet.

So, s = 2.5 when r = 30. Substitute:

$\displaystyle 2.5=\frac{k}{30}$

Solve for k:

$k=30(2.5)=75$

So, our equation is:

$\displaystyle s=\frac{75}{r}$

Then when the radius is three feet, r = 3. Evaluate for s:

$\displaystyle s=\frac{75}{(3)}=25\text{ feet per second}$

So, the speed of the water in a whirlpool with a radius of three feet is 25 feet per second.