A ferris wheel of radius 100 feet is rotating at a constant angular speed Ï rad/sec counterclockwise. using a stopwatch, the rid
er finds it takes 5 seconds to go from the lowest point on the ride to a point q, which is level with the top of a 44 ft pole. assume the lowest point of the ride is 3 feet above ground level.
1 answer:
Refer to the image below.
From the geometry, the height is calculated as follows: y = 100 - (44 - 3) = 59 ft.
Using the Pythagorean theorem,
x² = 100² - 59² = 6519
Thus, x = 80.07403 ft.
Now to find the central angle, θ,
cos θ = 59/100 = 0.59
Therefore, θ is approximately 53.84° or 0.9397 radians.
Next, we will calculate the arc length pq.
Arc length S = pq = 0.9394*100 = 93.94 ft.
Now, for angular velocity,
ω = (0.9397 radians)/(5 s) = 0.188 rad/s.
Let’s calculate tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s.
Finally, determine the time for one complete revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s.
Summary of results:
The angular velocity is 0.188 rad/s.
The tangential velocity measures 18.8 ft/s.
The duration for a single revolution is 33.4 seconds.
From the geometry, the height is calculated as follows: y = 100 - (44 - 3) = 59 ft.
Using the Pythagorean theorem,
x² = 100² - 59² = 6519
Thus, x = 80.07403 ft.
Now to find the central angle, θ,
cos θ = 59/100 = 0.59
Therefore, θ is approximately 53.84° or 0.9397 radians.
Next, we will calculate the arc length pq.
Arc length S = pq = 0.9394*100 = 93.94 ft.
Now, for angular velocity,
ω = (0.9397 radians)/(5 s) = 0.188 rad/s.
Let’s calculate tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s.
Finally, determine the time for one complete revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s.
Summary of results:
The angular velocity is 0.188 rad/s.
The tangential velocity measures 18.8 ft/s.
The duration for a single revolution is 33.4 seconds.
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