A catapult launches a rocket at an angle of 53.0° above the horizontal with an initial speed of 100. m/s. The rocket engine immediately starts a burn, and for 3.00 s the rocket moves along its initial line of motion with an acceleration of 30.0 m/s2. Then its engine fails, and the rocket proceeds to move in free-fall. Find (a) the maximum altitude reached by the rocket, (b) its total flight time, and (c) its horizontal range.