# If a rocket with a mass of 2900 tons vertically accelerates at a rate of # 2/9 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 6 seconds?

First work out what force the rocket is exerting to accelerate. Then use: Power = Force x Velocity.

The rocket's power is approximately 35.9 MW after 6 seconds.

Downward forces - upward forces equals the resultant upward force.

Now that we have a force expression, let's talk about the power:

Since you're from the USA, we'll refer to your tons as US tons, or short tons.

After six seconds, the rocket's power is thus roughly 35.9 MW.

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To calculate the power exerted by the rocket, you can use the formula:

Power = Force × Velocity

First, find the force exerted by the rocket using Newton's second law:

Force = Mass × Acceleration

Then, find the velocity of the rocket using the formula for uniform acceleration:

Velocity = Initial Velocity + Acceleration × Time

Substitute the given values into the equations and solve for the power.

Given: Mass (m) = 2900 tons = 2900000 kg Acceleration (a) = 2/9 m/s^2 Time (t) = 6 seconds

Using Newton's second law: Force = Mass × Acceleration

Using the formula for uniform acceleration to find velocity: Velocity = Initial Velocity + Acceleration × Time

Since the initial velocity is not given, we assume it's zero for simplicity.

Now, solve for the force and velocity:

Force = (2900000 kg) × (2/9 m/s^2) Force ≈ 644444.44 N

Velocity = 0 + (2/9 m/s^2) × (6 s) Velocity ≈ 4/3 m/s

Now, calculate the power:

Power = Force × Velocity Power ≈ (644444.44 N) × (4/3 m/s) Power ≈ 858,592.59 Watts

So, the rocket will have to exert approximately 858,592.59 Watts of power to maintain its acceleration after 6 seconds.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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