Final answer:
The initial acceleration of the rocket is 17.5 m/s². It takes approximately 1.90 seconds for the rocket to reach a velocity of 120 km/h. As the mass of the rocket decreases, the acceleration increases and the time to reach the desired velocity decreases.
Step-by-step explanation:
(a) To find the initial acceleration of the rocket, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration. The force produced by the rocket's engines is 3.50 x 107 N. Therefore, the initial acceleration can be calculated by dividing the force by the mass of the rocket:
Acceleration = Force/Mass = (3.50 x 107 N) / (2.00 x 106 kg) = 17.5 m/s2
(b) To calculate the time it takes for the rocket to reach a velocity of 120 km/h (33.33 m/s) straight up, we can use the equation of motion:
Velocity = Acceleration x Time
Time = Velocity / Acceleration = (33.33 m/s) / (17.5 m/s2) = 1.90 seconds
(c) As the mass of the rocket decreases significantly as its fuel is consumed, the acceleration and time for its motion would also change. The force produced by the engines remains constant, but the mass decreases. Therefore, the acceleration would increase according to Newton's second law, as the equation F = ma shows that acceleration is inversely proportional to mass. With a smaller mass, the rocket would experience a greater acceleration. As a result, the rocket would reach its desired velocity faster than if it had a larger initial mass.