If a rocket with a mass of 3500 tons vertically accelerates at a rate of # 1/5 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 15 seconds?
The given mass is assumed to be in metric tons.
We are asked to determine the power output that the rocket needs in order to maintain its acceleration for a predetermined period of time.
First, let's determine the rocket's mass in kilograms:
Therefore, its weight in newtons is
We are informed that the rocket's acceleration is
Therefore, the net force acting on the rocket according to Newton's second law is
There are just two forces influencing the rocket:
its mass (with a downward motion)
the thrust force acting upward that comes from the rocket
Using the net force equation, we can determine the thrust force:
We can now calculate the work that the thrust force does now that we know it:
We're given
Thus
As a result, the thrust force's work is
The thrust's power output is provided by
Thus
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To calculate the power exerted by the rocket, you can use the formula:
Power = Force × Velocity
First, calculate the force exerted by the rocket using Newton's second law:
Force = Mass × Acceleration
Given: Mass = 3500 tons Acceleration = 1/5 m/s²
After finding the force, you need to calculate the velocity of the rocket at 15 seconds using the formula:
Velocity = Initial Velocity + (Acceleration × Time)
Given: Initial Velocity = 0 m/s (assuming the rocket starts from rest) Acceleration = 1/5 m/s² Time = 15 seconds
Once you have the force and velocity, you can find the power using the formula:
Power = Force × Velocity
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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.
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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