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!
a. Well, 3 revolutions per minute means that the carousel completes 3 circles in 1 minute. Since the circumference of a circle is given by 2πr, where r is the radius, we can calculate the distance traveled by the carousel in 1 minute.
Let's convert the time to seconds. There are 60 seconds in a minute, so the carousel completes 3 revolutions in 60 seconds. That means it takes 20 seconds to complete 1 revolution.
The linear velocity is the distance traveled divided by the time taken. So, the linear velocity in feet per second is:
(2π * 22.5 feet) / 20 seconds = 7.1 feet per second.
Good job, you got it right!
b. To find the distance from the center of the carousel, we can use a similar approach. We know the linear velocity is 3.1 feet per second, and we want to find the radius (distance from the center).
Using the formula for the circumference of a circle again, we can rearrange it to solve for the radius:
2πr = linear velocity * time
Since we have the linear velocity in feet per second, and we want to find the radius in feet, let's choose a time of 1 second for simplicity.
2πr = 3.1 feet per second * 1 second
2πr = 3.1 feet
Now, let's solve for r:
r = 3.1 feet / (2π)
r ≈ 0.494 feet
The person on the inside of the carousel is approximately 0.494 feet from the center.
c. To find how much faster the rider on the outside is going than the rider on the inside, we can subtract their respective linear velocities.
The rider on the outside has a linear velocity of 7.1 feet per second, and the rider on the inside has a linear velocity of 3.1 feet per second.
Difference in linear velocities = 7.1 feet per second - 3.1 feet per second = 4 feet per second.
Therefore, the rider on the outside is going approximately 4 feet per second faster than the rider on the inside.
I hope that clarifies B and C for you!
Sure! Let's go step by step.
a. To find the linear velocity in feet per second, we can use the formula:
Linear Velocity (in ft/s) = 2πr * Revolutions per Minute
Given that the Kit Carson County Carousel makes 3 revs per minute and the person is riding a horse that is 22 1/2 feet from the center, let's calculate the linear velocity:
Radius (r) = 22.5 ft
Revolutions per Minute = 3
Linear Velocity = 2 * π * 22.5 * 3 / 60 (convert minutes to seconds)
Using a calculator, this simplifies to:
Linear Velocity = 7.066 ft/s (rounded to the nearest thousandth)
So, the linear velocity of someone riding a horse 22 1/2 feet from the center is approximately 7.066 ft/s.
b. To determine how far the person on the inside of the carousel is from the center, we need to rearrange the formula:
Linear Velocity (in ft/s) = 2πr * Revolutions per Minute
We are given the linear velocity of the person on the inside as 3.1 ft/s. Let's solve for the radius (r):
Radius (r) = Linear Velocity / (2π * Revolutions per Minute)
Substituting the given values:
Radius = 3.1 / (2π * 3)
Using a calculator and rounding to the nearest tenth, we get:
Radius = 0.165 ft
So, the person on the inside of the carousel is approximately 0.165 ft (or 1.98 inches) from the center.
c. To find how much faster the rider on the outside is going compared to the rider on the inside, we can subtract the linear velocity of the person on the inside from the linear velocity of the person on the outside:
The rider on the outside is going at a linear velocity of 7.066 ft/s (as calculated in part a), and the rider on the inside is going at a linear velocity of 3.1 ft/s (as given in the question).
Difference in Linear Velocities = Linear Velocity (Outside rider) - Linear Velocity (Inside rider)
Difference = 7.066 ft/s - 3.1 ft/s
Using a calculator, we get:
Difference = 3.966 ft/s (rounded to the nearest thousandth)
So, the rider on the outside is approximately 3.966 ft/s faster than the rider on the inside.
I hope this helps! Let me know if you have any further questions.
To solve parts B and C, we first need to understand the relationship between linear velocity, angular velocity, and radius.
Linear velocity (v) is the distance traveled per unit of time, typically measured in feet per second. It represents how fast an object is moving along its circular path.
Angular velocity (ω) is the rate at which an object rotates around a central axis, typically measured in radians per second. It represents how fast an object is rotating.
The relationship between linear velocity and angular velocity is given by the formula:
v = ω * r
where r is the radius of the circular path.
Now let's solve part B:
b. The linear velocity of the person on the inside of the carousel is 3.1 feet per second. We need to find the distance from the center of the carousel.
We know that the carousel makes 3 revolutions per minute. To find the angular velocity (ω) in radians per second, we can convert revolutions per minute to radians per second:
1 revolution = 2π radians
3 revolutions per minute = 3 * 2π radians per minute
To convert to radians per second, we divide by 60 (since there are 60 seconds in a minute):
3 * 2π / 60 radians per second = π/10 radians per second
Now we can rearrange the formula v = ω * r to solve for r:
3.1 = π/10 * r
To isolate r, divide both sides by π/10:
r = 3.1 / (π/10) ≈ 9.877 feet
Therefore, the person on the inside of the carousel is approximately 9.877 feet from the center.
Now let's solve part C:
c. We need to find the difference in linear velocities between the person on the outside and the person on the inside of the carousel.
We have already calculated the linear velocity of the person on the inside as 3.1 feet per second.
To find the linear velocity of the person on the outside, we can use the formula v = ω * r. The person on the outside is 22 1/2 feet from the center, so:
v = ω * 22.5
We know from part A that the carousel makes 3 revolutions per minute, which we converted to π/10 radians per second. Plugging in these values:
v = (π/10) * 22.5
v ≈ 7.07 feet per second (rounded to two decimal places)
The difference in linear velocities is then:
Δv = v_outer - v_inner
Δv = 7.07 - 3.1
Δv ≈ 3.97 feet per second
Therefore, the rider on the outside is approximately 3.97 feet per second faster than the rider on the inside.