Billy is riding on a 20 meter diameter Ferris wheel that is making 3 revolutions per minute. What are your linear velocity and your angular velocity? If there are 8 equally spaced seats on the ferris wheel then what is the length of the arc between two adjacent seats?

the circumference is 20pi meters. So, the linear velocity is 60pi m/min.

angular velocity is 2pi radians per revolution, so 6pi radians/min

you know the circumference. Divide that by 8 to get the distance between seats.

To find the linear velocity, we first need to determine the circumference of the Ferris wheel. The circumference of a circle can be found using the formula C = π * d, where C represents the circumference and d represents the diameter.

Given that the diameter of the Ferris wheel is 20 meters, we can calculate the circumference as follows:

C = π * d
C = π * 20
C ≈ 62.83 meters

The linear velocity is the distance traveled by an object in a given time.

Since the Ferris wheel is making 3 revolutions per minute, we can calculate the linear velocity by multiplying the circumference by the number of revolutions per minute:

Linear velocity = Circumference * Revolutions per Minute
Linear velocity = 62.83 * 3
Linear velocity ≈ 188.49 meters per minute

To find the angular velocity, we need to convert the revolutions per minute into radians per minute. Since there are 2π radians in one full revolution, we can multiply the number of revolutions per minute by 2π:

Angular velocity = Revolutions per Minute * 2π
Angular velocity = 3 * 2π
Angular velocity ≈ 18.85 radians per minute

Now, let's find the length of the arc between two adjacent seats.

Since there are 8 equally spaced seats on the Ferris wheel, the angle between two adjacent seats can be calculated by dividing the total angle of one complete revolution (2π radians) by the number of seats:

Angle between adjacent seats = (2π radians) / (number of seats)
Angle between adjacent seats = (2π radians) / (8 seats)
Angle between adjacent seats ≈ 0.7854 radians

The length of the arc between two adjacent seats can be found using the formula L = r * θ, where L represents the length of the arc, r represents the radius (half of the diameter), and θ represents the angle in radians.

Given that the diameter is 20 meters, the radius is half of that:

r = 20 / 2
r = 10 meters

Now we can calculate the length of the arc:

L = r * θ
L = 10 * 0.7854
L ≈ 7.854 meters

Therefore, the length of the arc between two adjacent seats is approximately 7.854 meters.