The third stage of a rocket is injected by its booster with a velocity u of 13180 km/h at A into an unpowered coasting flight to B. At B it rocket motor is ignited when the trajectory makes an angle of 25° with the horizontal. Operation is effectively above the atmosphere, and the gravitational acceleration during this interval may be taken as 8.97 m/s2, constant in magnitude and direction. Determine the time t to go from A to B. (This quantity is needed in the design of the ignition control system.) Also determine the corresponding increase h in altitude. Answers: t= h = 158.03 122.14 43° Horiz. S km -25° -Horiz.

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.