Question

A 30 kg rocket toy lifts off vertically from the ground. After 3 minutes, its engine stops. The rocket has then a speed of 320 m/s and is at an altitude of 2600 m.

a) What is the work done by the rocket engine?
b) What is the average power of the rocket engine?
A) 960,000 J, 5,333 W
B) 5,333 J, 960,000 W
C) 960,000 J, 960,000 W
D) 5,333 J, 5,333 W

Answer 1

The work done by the rocket engine is 7.5 × 10^6 J and the average power of the rocket engine is approximately 5,333 W.

Step-by-step explanation:

To answer the given questions:

a) The work done by the rocket engine can be calculated using the formula: Work = Force * Distance. In this case, the force is equal to the weight of the rocket, which can be calculated using the formula: Weight = mass * acceleration due to gravity. The distance is the change in the rocket's altitude. Therefore, the work done by the rocket engine is equal to the weight of the rocket multiplied by the change in altitude:

Work = Weight * Change in Altitude = (mass * acceleration due to gravity) * Change in Altitude = (30 kg * 9.8 m/s^2) * 2600 m = 7,548,000 J = 7.5 × 10^6 J.

b) The average power of the rocket engine can be calculated using the formula: Power = Work / Time. In this case, the work is the same as calculated in part (a), and the time is given as 3 minutes, which is equal to 180 seconds. Therefore, the average power of the rocket engine is:

Power = Work / Time = 7,548,000 J / 180 s = 41,933.33 W ≈ 5,333 W.