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 figure shown below.
From the geometry,
y = 100 - (44 - 3) = 59 ft
From the Pythagorean theorem,
x² = 100² - 59² = 6519
x = 8007403 ft
Calculate the central angle, θ.
cos θ = 59/100 = 0.59
θ = 53.84° = 0.9397 radians
Calculate the arc length pq.
S = pq = 0.9394*100 = 93.94 ft
Calculate the angular velocity.
ω = (0.9397 radians)/(5 s) = 0.188 rad/s
Calculate the tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s
Calculate the time for 1 revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s
Answers:
The angular speed is 0.188 rad/s
The tangential speed is 18.8 ft/s
The time for one revolution is 33.4 s
From the geometry,
y = 100 - (44 - 3) = 59 ft
From the Pythagorean theorem,
x² = 100² - 59² = 6519
x = 8007403 ft
Calculate the central angle, θ.
cos θ = 59/100 = 0.59
θ = 53.84° = 0.9397 radians
Calculate the arc length pq.
S = pq = 0.9394*100 = 93.94 ft
Calculate the angular velocity.
ω = (0.9397 radians)/(5 s) = 0.188 rad/s
Calculate the tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s
Calculate the time for 1 revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s
Answers:
The angular speed is 0.188 rad/s
The tangential speed is 18.8 ft/s
The time for one revolution is 33.4 s
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