Use of calculus in a launch of a rocket - Relevant Assumptions

[Saba]

Homework Statement

Hi, I'm working on my year-12 math report. In this report we are modelling and discussing the appropriateness of the potential behavior of rocket's velocity, using some mathematical functions provided to us. then we develop a further function ourselves, based on the altitude the rocket has achieved at any given time in the flight.

Relevant Equations

the math models we had to investigate are:

v(t)=bsin(t)
v(t)=dIn(gt^3+h)+kt
v(t)=mte^((nt-p) )+q

I know that we have to assume certain things for the math to be achievable (at my level). for instance, I assumed that the rocket goes in a straight line instead of orbiting around the earth at an angle. but I can't develop any further assumptions as the task is so generalised and open-ended.
Can someone please help me figure out what other assumptions are necessary to do the math of this report?

 

[Saba]

I know that we have to assume certain things for the math to be achievable (at my level). for instance, I assumed that the rocket goes in a straight line instead of orbiting around the earth at an angle. but I can't develop any further assumptions as the task is so generalised and open-ended.
Can someone please help me figure out what other assumptions are necessary to do the math of this report?

 

[Filip Larsen]

Are you able to establish what altitude function the three different velocity functions result in? If not, do you have an idea how to obtain them?
Regarding appropriateness, it sounds like it is a more open part of the assignment where you yourself have to formulate some selection criteria that would make one type of rocket more appropriate than the others. There should be some obvious criteria you can use, but I assume it is within the assignment scope to use any criteria as long as you argue well for why it is appropriate.

Note that at PF, as you seem to already be aware of, do not give direct answers to assignment, but we can help you figure out how to calculate the answers yourself once you have shown you have made an effort to solve it yourself. This also means much of the help you receive here will be in the form of questions.

 

[PhDeezNutz]

I think you are right. Without further information I think we have to assume the rocket travels in a straight line. Try integrating each of those functions to get position.

Notice if you integrate sine you get (negative) cosine. Is this a reasonable result? I mean what is the point of a rocket going up and down continuously between two points. Therefore the first option is not a valid velocity function for something that needs to be traveling upwards constantly.

Carry out the same analysis with the other functions.

 

[PeroK]

Homework Statement: Hi, I'm working on my year-12 math report. In this report we are modelling and discussing the appropriateness of the potential behavior of rocket's velocity, using some mathematical functions provided to us. then we develop a further function ourselves, based on the altitude the rocket has achieved at any given time in the flight.
Relevant Equations: the math models we had to investigate are:

v(t)=bsin(t)
v(t)=dIn(gt^3+h)+kt
v(t)=mte^((nt-p) )+q

I know that we have to assume certain things for the math to be achievable (at my level). for instance, I assumed that the rocket goes in a straight line instead of orbiting around the earth at an angle. but I can't develop any further assumptions as the task is so generalised and open-ended.
Can someone please help me figure out what other assumptions are necessary to do the math of this report?

I would differentiate to get the acceleration as a function of time in each case. Not least because, in general, differentiation is easier than integration. But also, because acceleration is related to force/thrust and that's why a rocket needs an engine.

That said, only one of those functions looks at all viable to me.

 

[PhDeezNutz]

Yup I have to agree with @PeroK . While this is not a super technical investigation. Differentiating (and integrating) each of those functions will help you see which one of those is at least sensible. Even if they may not be exactly correct.

I think that was the point.

Also graph each derivative and anti derivative to gain insight. I think this was implied in other posts but I’d just like to emphasize it.

If you do this and summarize your interpretations I think you have more than enough to fulfill the requirements of your (open ended) high school project.