Your horse on a merry-go-round is 18.3 m from the center. Suppose the merry-go-round makes 12.4 rev per ride. If you take 3 rides, through what angle do you move and how many meters do you travel?
3 rides = 3 * 12.4 = 37.2 revolutions
So, the angle moved is 2pi * 37.2 = ? radians
The distance traveled is 2pi * 37.2 * 18.3 = ? meters
To find the angle through which you move on the merry-go-round, you can use the formula:
θ = 2πn
Where θ is the angle in radians, π is approximately 3.14159, and n is the number of revolutions.
In this case, the merry-go-round makes 12.4 revolutions per ride, so the angle traversed for one ride is:
θ = 2π * 12.4 = 24.8π radians
To find the angle traversed in three rides, you can simply multiply the angle traversed for one ride by three:
θ_total = 3 * θ = 3 * 24.8π = 74.4π radians
Now, to find the meters traveled, you can use the formula:
s = rθ
Where s is the distance traveled, r is the distance from the center, and θ is the angle in radians.
In this case, the horse is 18.3 meters from the center, and the total angle traversed is 74.4π radians. So, the distance traveled is:
s = 18.3 * 74.4π = 1356.72π meters
Approximating π as 3.14159, the distance traveled would be:
s ≈ 1356.72 * 3.14159 ≈ 4266.14 meters
Therefore, by taking 3 rides on the merry-go-round, you would move through an angle of 74.4π radians and travel approximately 4266.14 meters.