An expression for the vertical velocity as a function of time

In summary, the problem involves a rocket being launched vertically upwards from rest, burning fuel at a constant rate, and experiencing buoyancy and gravitational acceleration. The goal is to derive an expression for the vertical velocity of the rocket as a function of time before the fuel runs out. The solution requires effort and possibly the use of definite or indefinite integrals.
  • #1
Physil
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New user has been reminded to show their work on schoolwork questions
A rocket of initial mass m0 is launched vertically upwards from the rest. The rocket burns fuel at the constant rate m', in such a way, that, after t seconds, the mass of the rocket is m0-m't. With a constant buoyancy T, the acceleration becomes equal to a=T/(m0-m't) -g. The atmospheric resistance can be neglected, and the gravitational accelereation ,g, is considered a constant for low-level flights. Deduce an expression for the vertical velocity v of the rocket, as a function of time t, before the fuel burns out completely.
 
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  • #2
What are your ideas about the problem?
 
  • #3
We're not here to solve physics problems for you. We're here to help YOU solve them. You have to make an effort towards a solution. If you need a hint to get started, acceleration is the time derivative of velocity.
 
  • #4
Mister T said:
We're not here to solve physics problems for you. We're here to help YOU solve them. You have to make an effort towards a solution. If you need a hint to get started, acceleration is the time derivative of velocity.
I'm sorry. I new here. That's exactly what I was thinking. I just don't know if I should use definite or indefinite integral.
 
  • #5
Physil said:
I'm sorry. I new here. That's exactly what I was thinking. I just don't know if I should use definite or indefinite integral.
Why would you use an indefinite integral? Does the integration have a starting point and stopping point?
 
  • #6
Physil said:
I just don't know if I should use definite or indefinite integral.
Try it both ways and see. It doesn't take that much time.
 

1. What is the equation for vertical velocity as a function of time?

The equation for vertical velocity as a function of time is v(t) = v0 + at, where v0 is the initial velocity and a is the acceleration due to gravity.

2. How is the equation for vertical velocity derived?

The equation for vertical velocity is derived from the fundamental principles of kinematics, specifically the equations of motion. It takes into account the initial velocity, the acceleration due to gravity, and the time elapsed.

3. What is the significance of the vertical velocity equation?

The vertical velocity equation is significant because it allows us to calculate the instantaneous velocity of an object at any given time during its motion. This is important in understanding the motion of objects and predicting their future positions.

4. Can the vertical velocity equation be applied to all objects?

Yes, the vertical velocity equation can be applied to all objects as long as they are experiencing a constant acceleration due to gravity. This is true for objects in free fall near the surface of the Earth.

5. How is the vertical velocity equation used in real-world applications?

The vertical velocity equation is used in various real-world applications, such as in the design of roller coasters and other amusement park rides, in predicting the trajectory of projectiles, and in understanding the motion of objects in free fall. It is also used in physics experiments and in the study of motion and mechanics.

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