In Prob. 13.110, the speed of the space vehicle was

Chapter 13, Problem 13.111

(choose chapter or problem)

In Prob. 13.110, the speed of the space vehicle was decreased as it passed through A by firing its engine in a direction opposite to the direction of motion. An alternative strategy for taking the space vehicle out of its circular orbit would be to turn it around so that its engine would point away from the earth and then give it an incremental velocity \(\Delta \mathbf{v}_{A}\) toward the center O of the earth. This would likely require a smaller expenditure of energy when firing the engine at A, but might result in too fast a descent at B. Assuming this strategy is used with only 50 percent of the energy expenditure used in Prob. 13.110, determine the resulting values of \(f_{B}\) and \(v_{B}\).