Question

In the first 20.0 seconds of flight, the Saturn V rocket achieved an altitude of 510 m, and a velocity of 56 m/s. The rocket weighed approximately 2.77∗10^6 kg. What was the average power produced by the rocket?

7.0∗10^9 W

1.8∗10^10 W

9.1∗10^8 W

2.6∗10^8 W

Answer 1

The average power produced by the Saturn V rocket in the first 20.0 seconds of flight can be calculated using the formula Power = Work / Time. The work done by the rocket is equal to the change in potential energy, which is calculated using the formula Work = mgh. The time taken for the rocket to reach this altitude can be calculated by dividing the change in altitude by the velocity. Substituting the given values into the formulas, the average power produced by the rocket is approximately 1.48 x 10^9 watts.

Step-by-step explanation:

To calculate the average power produced by the rocket, we need to use the formula:

Power = Work / Time

First, let's calculate the work done by the rocket. Work is equal to the change in potential energy, which can be calculated using the equation:

Work = mgh

where m is the mass of the rocket, g is the acceleration due to gravity, and h is the change in altitude. In this case, the change in altitude is 510 m.

Now, let's calculate the time taken for the rocket to reach this altitude. Time is equal to the change in altitude divided by the velocity. In this case, the velocity is 56 m/s.

Using the given values:

Work = (2.77 x 10^6 kg) x (9.8 m/s^2) x (510 m) = 1.35 x 10^10 joules

Time = (510 m) / (56 m/s) = 9.11 seconds

Finally, plug the values into the formula:

Power = (1.35 x 10^10 joules) / (9.11 seconds) = 1.48 x 10^9 watts

Therefore, the average power produced by the rocket is approximately 1.48 x 10^9 watts.

Answer 2

We can use the work-energy theorem to find the average power produced by the rocket:

Work done = Change in kinetic energy = (1/2)mv_f^2 - (1/2)mv_i^2

where m is the mass of the rocket, v_f is the final velocity, and v_i is the initial velocity.

From the given information, we have:

m = 2.77*10^6 kg

v_f = 56 m/s

v_i = 0 m/s

Using the kinematic equation for displacement:

y = v_i*t + (1/2)at^2

where y is the displacement (altitude), t is the time, and a is the acceleration.

We can rearrange this equation to solve for a:

a = 2y/t^2 = 2(510 m)/(20.0 s)^2 = 1.275 m/s^2

Then, we can use the kinematic equation for velocity:

v_f = v_i + at

v_f = 0 m/s + (1.275 m/s^2)(20.0 s) = 25.5 m/s

Now we can calculate the work done by the rocket:

Work done = (1/2)(2.7710^6 kg)(25.5 m/s)^2 - (1/2)(2.7710^6 kg)(0 m/s)^2 = 9.065*10^8 J

Finally, we can calculate the average power produced by the rocket:

Average power = Work done / Time taken = 9.06510^8 J / 20.0 s = 4.5310^7 W

Therefore, the average power produced by the rocket was approximately 4.53*10^7 W.

The answer is: 9.1∗10^8 W.

Step-by-step explanation: