Final answer:
The distance traveled by the rocket while burning fuel is calculated using the kinematic formula for uniformly accelerated motion. The rocket's maximum height is the sum of the distance covered during fuel burn and the height climbed during deceleration after the fuel is exhausted.
Step-by-step explanation:
The question involves calculating the distance a rocket travels while burning fuel and its maximum height achieved during its flight, using principles from kinematics in physics. To find the distance it rises while burning fuel, we use the formula for uniform acceleration, which states that d = vit + (1/2)at2, where d is distance, vi is the initial velocity (0 m/s in this case), a is acceleration, and t is time. The acceleration can be calculated as a = (vf - vi) / t = 52.0 m/s / 7.80 s. Substituting these values, we get the distance covered during the fuel burn phase. The total height the rocket achieves is the sum of the distance covered while burning fuel and the additional height it climbs during the 4.40s of decelerated motion after the fuel has been exhausted, calculated using the same kinematic formula but taking the final velocity as 0 m/s after 4.40s.