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,
[tex]\rm y = 100-(44-3)=59 \; ft[/tex]
y = 59 ft
Now applying pythagorean theorem,
[tex]x^2 + 59 ^2= 100^2[/tex]
[tex]x=\sqrt{100^2-59^2}[/tex]
[tex]\rm x = 80.7403\;ft[/tex]
Now to calculate angle [tex]\theta\\[/tex],
[tex]\rm cos\theta = \dfrac{59}{100}=0.59[/tex]
[tex]\rm \theta = 53.84^\circ=0.9397\;radians[/tex]
Now the arc length pq is given by,
[tex]\rm S =pq=0.9397\times100[/tex]
[tex]\rm S = 93.97\; ft[/tex]
Now the angular velocity is given by,
[tex]\omega = \dfrac {0.9397}{5}[/tex]
[tex]\rm \omega = 0.188\;rad/sec[/tex]
Now the tangential velocity is given by,
[tex]\rm v={100}\times{0.188}[/tex]
[tex]\rm v = 18.8\;ft/sec[/tex]
Now the time for a single revolution is given by,
[tex]\rm T = \dfrac{2\pi}{0.188}[/tex]
[tex]\rm T= 33.4\; sec[/tex].
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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https://brainly.com/question/17592191?referrer=searchResults
