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. What is the acceleration of the empty bottom stage?

1) 4.9 m/s��
2) 9.8 m/s��
3) 49 m/s��
4) 98 m/s��

Answer 1

The acceleration of the empty bottom stage is 49 m/s², the same as the acceleration of the top stage.

Step-by-step explanation:

The acceleration of the empty bottom stage can be found using the concept of the rocket equation. The equation states that the change in velocity of a rocket is equal to the exhaust velocity multiplied by the natural logarithm of the ratio of the initial mass to the final mass. In this case, the final mass is the mass of the top stage and the initial mass is the sum of the masses of the top and bottom stages. Since the bottom stage is 10 times less massive than the top stage, the final mass can be approximated as the mass of the top stage. Given that the exhaust velocity is constant, the acceleration of the empty bottom stage will be the same as the acceleration of the top stage, which is 49 m/s².