The third stage of a rocket is injected by its booster with a velocity u of 15 000 km/...

The third stage of a rocket is injected by its booster with a velocity u of 15 000 km/h at A into an unpowered coasting flight to B. At B its rocket motor is ignited when the trajectory makes an angle of 20^o with the horizontal. Operation is effectively above the atmosphere, and the gravitational acceleration during this interval may be taken as 9 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.