A ferris wheel has a diameter of 100m and the bottom of the wheel is 4m above the ground. It rotates two times every 10 minutes. Using this information, complete each question.
c) Determine the angular velocity of the Ferris wheel in radians/second
d)How far (in meters) has the Ferris wheel travelled after 6 min?
Thank you, any help is really appreciated!
d) With a d=100 we know that the distance the wheel travels C=pi(d) so
c=3.14159(100m)
c=approx 314m to go around the ferris wheel once.
But you can go twice 314(2) in 10 min
so...
setting up a proportion
distance/time = distance/time
618m/10min = x/6 min
and solve for x
two turns every 10 minutes means
2rev/10min * 2πrad/rev * 1min/60s = 4π/600 rad/s
Thank you both so much!
To find the angular velocity of the Ferris wheel in radians/second, we need to know the time it takes for one complete rotation.
Since the Ferris wheel rotates two times every 10 minutes, it means it completes one full rotation in 10 minutes/2 = 5 minutes.
To convert the time to seconds (since radians/second is the desired unit), we multiply by 60 since there are 60 seconds in a minute:
5 minutes * 60 seconds/minute = 300 seconds.
So the Ferris wheel takes 300 seconds to complete one full rotation.
The circumference of the Ferris wheel is equal to the distance it travels in one rotation, which is given by the formula:
C = π * diameter.
Substituting the given diameter of 100m, we get:
C = 3.14 * 100m = 314m.
Therefore, in one rotation, the Ferris wheel travels a distance of 314 meters.
To find how far the Ferris wheel has traveled after 6 minutes, we need to determine the number of rotations it has completed in 6 minutes. Since we know it takes 5 minutes to complete one rotation, we can divide the given time by 5:
6 minutes / 5 minutes/rotation = 1.2 rotations.
Since we have the number of rotations, we can calculate the distance traveled by multiplying it by the circumference of the wheel:
1.2 rotations * 314m/rotation = 376.8m.
Therefore, after 6 minutes, the Ferris wheel has traveled a distance of 376.8 meters.