An expression for the vertical velocity as a function of time

AI Thread Summary
The discussion revolves around deriving the vertical velocity of a rocket as a function of time, considering its changing mass due to fuel consumption. The rocket's acceleration is defined as a = T/(m0 - m't) - g, where T is the constant buoyancy and g is the gravitational acceleration. Participants emphasize the importance of understanding the relationship between acceleration and velocity, suggesting that acceleration is the time derivative of velocity. There is a debate on whether to use definite or indefinite integrals for the calculations, with encouragement to try both methods. The overall focus is on guiding individuals to engage actively in solving the physics problem themselves.
Physil
Messages
2
Reaction score
0
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.
 
Physics news on Phys.org
What are your ideas about the problem?
 
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.
 
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.
 
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?
 
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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Electric field due to charges between 2 parallel infinite planes'

TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
View full post »

Similar threads

Rocket acceleration problem: confused about Newton's 2nd Law
Replies
42
Views
5K
How to calculate velocity of infinite-stage rocket?
Replies
2
Views
1K
Pytels Dynamics 12.39: A rocket is launched vertically
Replies
3
Views
2K
Why is the thrust equation same under gravitational force?
Replies
10
Views
2K
Force and acceleration of a rocket
Replies
3
Views
2K
Oblique soccer shot calculation task
Replies
38
Views
4K
Using differentiation to find a general expression
Replies
2
Views
2K
Calculate Thrust of Rocket: Homework Statement
Replies
2
Views
3K
How Does the Relativistic Rocket Equation Describe Velocity?
Replies
2
Views
2K
Forces - Space Shuttle Takeoff Calculations
Replies
22
Views
2K

Hot Threads

Recent Insights

Back
Top