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The earth's radius is about 4000 miles. kampala, the capital of uganda, and singapore are both nearly on the equator. the distance between them is 5000 miles as measured along the earth's surface. part a the flight from kampala to singapore takes 8.3 hours. what is the plane's angular velocity relative to the earth's surface? give your answer in â/h.

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shinmin
To compute for Earth's circumference it is 2*pi*r (radius is equal to 4,000 miles) which is equal to 25,130 miles 25,130 miles corresponds to 360º, so 5,000 miles corresponds to 360 * 5000/25130 = 71.6º 
71.6º is equivalent to 71.6* 2pi / 360=1.25 radians

Angular velocity is 1.25/ 8.3 =0.151 rad/h  

Plane's angular velocity relative to the earth's surface = 0.15 rad/hr

Explanation:

Radius of earth, r = 4000 miles

Angular velocity is the ratio of linear velocity and radius.

         [tex]\omega =\frac{v}{r}[/tex]

Linear distance from Kampala to Singapore = 5000 miles

Time taken = 8.3 hours

         Distance = Time x Velocity

         5000 = 8.3 x Velocity

         Velocity, v = 602.41 mph

Substituting in angular velocity equation

        [tex]\omega =\frac{v}{r}=\frac{602.41}{4000}=0.15rad/hr[/tex]

Plane's angular velocity relative to the earth's surface = 0.15 rad/hr

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