Physics, 04.07.2019 03:00 angellove1707

Aferris wheel of radius 100 feet is rotating at a constant angular speed ï rad/sec counterclockwise. using a stopwatch, the rider 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.

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Answers

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

Aferris wheel of radius 100 feet is rotating at a constant angular speed ï rad/sec counterclockwise.

Aferris wheel of radius 100 feet is rotating at a constant angular speed ï rad/sec counterclockwise.

Answer from: sarah19Nursing

Angular speed is 0.188 rad/s ,

Tangential speed is 18.8 ft/s ,

Time for one revolution is 33.4 s.

Given :

Ferris wheel of radius 100 ft.

The lowest point of the ride is 3 feet above ground level.

Solution :

Refer the attached diagram for better understanding.

From the diagram we know that,

$\rm y = 100-(44-3)=59 \; ft$

y = 59 ft

Now applying pythagorean theorem,

x^2 + 59 ^2= 100^2

$x=\sqrt{100^2-59^2}$

$\rm x = 80.7403\;ft$

Now to calculate angle $\theta\\$ ,

$\rm cos\theta = \dfrac{59}{100}=0.59$

$\rm \theta = 53.84^\circ=0.9397\;radians$

Now the arc length pq is given by,

$\rm S =pq=0.9397\times100$

$\rm S = 93.97\; ft$

Now the angular velocity is given by,

$\omega = \dfrac {0.9397}{5}$

$\rm \omega = 0.188\;rad/sec$

Now the tangential velocity is given by,

$\rm v={100}\times{0.188}$

$\rm v = 18.8\;ft/sec$

Now the time for a single revolution is given by,

$\rm T = \dfrac{2\pi}{0.188}$

$\rm T= 33.4\; sec$ .

Therefore, angular speed is 0.188 rad/sec , tangential speed is 18.8 ft/s ec and time for one revolution is 33.4 sec.

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