A shuttle is to rendezvous with a space station which is

Chapter 13, Problem 13.194

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A shuttle is to rendezvous with a space station which is in a circular Review Problems orbit at an altitude of 250 mi above the surface of the earth. The shuttle has reached an altitude of 40 mi when its engine is turned off at point B. Knowing that at that time the velocity \(v_{0}\) of the shuttle forms an angle \(f_{0}=55^{\circ}\) with the vertical, determine the required magnitude of \(v_{0}\) if the trajectory of the shuttle is to be tangent at A to the orbit of the space station.