If time to revolve around earth by a rocket is 3601 whats its velocity

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you mean speed, scalar quantity..
Speed will depend on altitude above Earth's surface, direction of travel against rotation or in the direction of rotation of Earth around it self.. What is the unit for time given? 3601 seconds or minutes.
it depends whether the rocket flies along the equator or at any other lattitude.

Answers

2014-11-12T14:51:05+05:30

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Let us say the altitude h at which the rocket flies is very small compared to radius of Earth.  Let us also assume that rocket flies above the equator and along the equator.  Let us assume that given time duration is in seconds.

Let the rocket fly from west to East, along the rotational direction of Earth.  Then the relative linear speed of rocket wrt to an object stationary on Earth will be:

  Relative linear speed = v = 2 π Re / time duration = 2π *6400 km / 3601 sec
        = 11.16 km/sec

  angular velocity of a stationary object on Earth's surface = 2π/(24*3600) rad/sec
             ω₀ = 7.272 * 10^-7  rad/sec
  Its linear speed will be V₀ = 465.42 meters/sec

  Speed of rocket (wrt to Sun, an inertial frame of reference)
           = 11.16 + 0.465 km/sec   = 11.625 km/sec
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Suppose the rocket flies in the direction East to West against rotation of Earth.  Then rocket actually does not cover full circumference in its orbit.  An object stationary on Earth also moves some distance in time of 3601.  But the relative speed remains same as before.

we find the absolute speed of rocket wrt Sun,

     distance covered by rocket in 3601 sec = 
           v * 3601 + (3,601/86,400) * 2 π 6400 = 2 π 6400

            then  v  = 10.70 km /sec   

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