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

25 feet per second.

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=(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=(k)/(30)`

Solve for k:

`k=30(2.5)=75`

So, our equation is:

`\displaystyle s=(75)/(r)`

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

`\displaystyle s=(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.