The Kit carson county carousel makes 3 revs per minute.

a. Find the linear velocity in feet per second of someone riding a horse that is 22 1/2 feet from the center.

Answer- I got 7.1 ft/s...

b. The linear velocity of the person on the inside of the carousel is 3.1 feet per second. How far is the person from the center of the carousel?

c. How much faster is the rider on the outisde going than the rider on the inside.

I need help with B and C. THanks!

All right, the exact answer for the first one is (9pi/4)...

You did (6pi)(22.5)/60. That reduces to 22.5pi / 10.

The thing that is changing is 22.5.
(x)(pi) / 10 = 3.1
(x)(pi) = 31
x = 31/pi = 9.87 ft

For c, you're just subtracting 3.1 from 7.1 to get 4 ft/s.

I hope that's helpful. (I'm 90% sure it's right.)

My weak point is these angular and linear velocities. -_- Sorry, Gabriel.

If you tell me how you got the first answer (and are sure you're right), then maybe I could help.

For a, i multiplied 3 x 2pi x 22.5 and got 424.1

Then i divided 424.1 by 60 and got 7.1 ft/s

To solve parts B and C of the problem, we'll need to use the concept of angular speed and linear speed.

Angular speed is the rate of change of angle with respect to time, measured in radians per second. In this case, the carousel makes 3 revolutions per minute, which means its angular speed is 3 times 2π radians per minute.

Linear speed, on the other hand, is the distance traveled per unit of time, measured in feet per second. It is related to angular speed by the formula:

Linear speed = Angular speed * Radius

where the radius is the distance from the center of rotation to the person.

Now let's move on to solving the problem!

b. To find the distance the person on the inside of the carousel is from the center, we can use the given linear speed (3.1 ft/s). Rearranging the formula, we have:

Radius = Linear speed / Angular speed

The angular speed can be calculated by converting 3 revolutions per minute to radians per second. There are 2π radians in one revolution, and 60 seconds in one minute. So the angular speed is:

Angular speed = (3 revolutions/minute) * (2π radians/revolution) / (60 seconds/minute)

Now substitute the values into the formula to find the radius:

Radius = 3.1 ft/s / (angular speed)

c. To find how much faster the rider on the outside is going compared to the rider on the inside, we need to compare their linear speeds. Recall that the linear speed is directly proportional to the radius. So, we can set up a ratio of their linear speeds:

Speed on the outside / Speed on the inside = Radius on the outside / Radius on the inside

Substitute the given values into the equation and solve for the speed on the outside.

Now, let's calculate the values for parts B and C.