Question

A two-stage rocket is launched vertically. After the bottom stage separates from the top stage and falls away, the top stage ignites its engines and continues to accelerate upwards. The top stage continues upwards with an acceleration of [49 m/s��]. The top stage is [10] times more massive than the empty bottom stage. Consider the system to be the top and bottom stages of the rocket together. Determine the magnitude of the acceleration of the center of mass of the system.

Answer 1

The magnitude of the acceleration of the center of mass of the system is zero.

Step-by-step explanation:

To determine the magnitude of the acceleration of the center of mass of the system, we can use the principle of conservation of momentum. The initial momentum of the system is zero because both stages of the rocket are initially at rest. After the bottom stage separates, the top stage ignites its engines and continues upwards with an acceleration of 49 m/s². The top stage is 10 times more massive than the empty bottom stage.

Using the equation F = ma, we can find the force exerted by the top stage on the center of mass of the system. The force is equal to the product of the mass of the top stage and its acceleration: F = (10 * mass of bottom stage) * (49 m/s²). The force exerted by the bottom stage falling away is equal in magnitude but opposite in direction. Therefore, the total force acting on the center of mass of the system is zero.

Since the total force is zero, the center of mass of the system does not accelerate. The magnitude of the acceleration of the center of mass of the system is therefore zero.