# Solving a Model Rocket Launch Problem

• Abscissas
In summary, the conversation is about solving a physics problem involving a model rocket launched with an initial speed of 50 m/s and an acceleration of 30 m/s2 until its engines stop at an altitude of 150 m. The problem involves finding the time the rocket is in the air and its final velocity. The conversation discusses using equations and manipulating variables to solve the problem. The final solution involves using the second and fourth equations to find the time and final velocity, and then using the fifth equation to find the distance the rocket has traveled at the time of landing.
Abscissas
Hello loves, I know there are post very very similar to this, but I just needed some help understanding it. any help is truly appreciated.

1. Homework Statement

A model rocket is launched straight upward with an initial speed of 50 m/s. It accelerates with a constant upward acceleration of 30 m/s2 until its engines stop at an altitude of 150 m. How long is the rocket in the air?

Vi= 50m/s
Vf= ??
a= 30 m/s^2
Change in y= 150

## The Attempt at a Solution

Alright so, I think to solve this problem, its a 2 step thing, this is caused because of the 2 accelerations, one from the rocket's fuel, and then once it empties, the second one from Earth's gravitational acceleration. I know I have 3 givens so I can find the other 2 variables. Alright this has led me to choosing the fourth and first equation. Although I am not sure if i can replace the delta x with delta Y, because the rocket would be going up into the air vertically, so it would be y instead of x right? this is where i am stuck, i don't really know what to do once i get to this point.

a preemptive thank you guys for the help

The particular symbols used to represent quantities aren't as important as the equation matching the given situation. Here you have motion in a straight line with constant acceleration(s). The equations you've shown match the scenario, so feel free to change Δx to Δy, or y, or z for that matter.

Abscissas
Alright, so, the Δx is replaceable, that is a good thing to know. Alright so I have been manipulating all of these equations to try to isolate time. So for the first part, I am trying to find out how long it takes to get to 150 meters. I have yet to find this equation, or been able to manipulate these 4 to give it to me. for the second part, I can find the Final velocity of the first part, and make that the initial velocity, and the final velocity of the second one will be 0 correct? because it would hit the floor coming to a stop. So once again i have to isolate t, but this time i have the following variables:
Yi = 150 meters
Yf= 0
a=-9.8 m/s^2
Vi= Vf of part 1

Abscissas said:
Alright, so, the Δx is replaceable, that is a good thing to know. Alright so I have been manipulating all of these equations to try to isolate time. So for the first part, I am trying to find out how long it takes to get to 150 meters. I have yet to find this equation, or been able to manipulate these 4 to give it to me. for the second part, I can find the Final velocity of the first part, and make that the initial velocity, and the final velocity of the second one will be 0 correct? because it would hit the floor coming to a stop. So once again i have to isolate t, but this time i have the following variables:
Yi = 150 meters
Yf= 0
a=-9.8 m/s^2
Vi= Vf of part 1
In a constant acceleration problem, there are typically five variables: initial speed, final speed, acceleration, distance and time. Given any three you can calculate the remaining two. Accordingly, there are five SUVAT equations, each involving four variables.
For the 150m stage, which three variables are known? Pick the equation that involves those three and time.
But you will anyway be needing to calculate the speed at that altitude too.

Abscissas
Okay, so i used the second equation to to solve for t, using the quadratic formula. so i got that t=1.90793s. I then used the fourth equation to solve for Vf which came out to be Vf=107.238 m/s. So now I am left only with 2 variables, Vf which now becomes Vi since i am now at the second phase where the engine stops. The second one i have is -g which is -9.8 m/s^2. I know I am overlooking something but I just can't figure it out. Unless Δy is the other variable, but I only have it as initial at 150 for phase 2, and I am not told it started from the ground, infact i am kind of told its not, because it is already going at a velocity of 50m/s. So i am not sure what to do

Abscissas said:
Okay, so i used the second equation to to solve for t, using the quadratic formula. so i got that t=1.90793s. I then used the fourth equation to solve for Vf which came out to be Vf=107.238 m/s. So now I am left only with 2 variables, Vf which now becomes Vi since i am now at the second phase where the engine stops. The second one i have is -g which is -9.8 m/s^2. I know I am overlooking something but I just can't figure it out. Unless Δy is the other variable, but I only have it as initial at 150 for phase 2, and I am not told it started from the ground, infact i am kind of told its not, because it is already going at a velocity of 50m/s. So i am not sure what to do
It's now at 150m. What will y be when it lands?

Abscissas
Well it would be 0, because it lands right? So -150 would be Δy? this wouldn't make sense though because it would continue to go up for a little bit before it would start to go back down, right?

Abscissas said:
Well it would be 0, because it lands right? So -150 would be Δy? this wouldn't make sense though because it would continue to go up for a little bit before it would start to go back down, right?
That doesn't matter, the equations will take care of it. The acceleration is constant from the time the engines stop until it hits the ground. Note that you will get a quadratic equation for that time, but only one solution will make sense.

Abscissas

I know it seems to be cleared up, but a classmate I was working it wasn't able to follow the thread that well, so I'll shorthand the steps below in case anyone else is having the same issues with this.

1) Engines push rocket up from the ground to an altitude of 150 m. You will need to find the final Velocity at that height because that will be the initial velocity used when calculating the rocket at freefall in the 2nd part of this problem.
2) Know that time is the only variable you don't have here - so use the one equation where t isn't included!
3) Remember initial velocity and initial distance is nothing pre-launch.
4) Now, calculate max height of rocket in freefall. Note that the initial Y will be where the rocket engines cut off, and the initial velocity will also be where the rocket cuts off. Also note that you are looking for max height in this problem (aka: where the rocket stops going upwards and starts to fall down). So the velocity during that change is zero (no longer moving up and not yet moving down). Again, plug into the one equation where t is not a variable.

Hope that helps!

CWatters

## 1. How do I determine the optimal angle for launching a model rocket?

The optimal angle for launching a model rocket depends on several factors, including the weight and design of the rocket, wind conditions, and the desired altitude. It is best to consult a launch angle chart or use a launch angle calculator to find the most suitable angle for your specific rocket and launch site.

## 2. What is the recommended engine size for a model rocket launch?

The recommended engine size for a model rocket launch depends on the weight of the rocket and the desired altitude. It is important to choose an engine that is not too powerful for the rocket, as this can result in damage or loss of the rocket. Consult a rocket motor guide or seek advice from experienced rocket enthusiasts for the best engine size for your rocket.

## 3. How do I calculate the maximum altitude my model rocket can reach?

To calculate the maximum altitude of a model rocket, you will need to know the weight of the rocket, the engine size, and the launch angle. You can use a rocket altitude calculator or use the following formula: Maximum Altitude = (Engine Thrust x Engine Burn Time) / (Rocket Weight x Launch Angle). Keep in mind that this is an estimate and actual results may vary.

## 4. What can I do if my model rocket consistently fails to launch properly?

If your model rocket consistently fails to launch properly, there are a few things you can try. First, make sure the rocket is assembled correctly and all parts are securely attached. Check the engine size and launch angle to make sure they are appropriate for your rocket. You may also need to adjust the stability of the rocket by adding or removing weight from the nose cone or fins.

## 5. How can I ensure a safe and successful model rocket launch?

To ensure a safe and successful model rocket launch, it is important to carefully follow all safety guidelines and regulations. Choose a suitable launch site with plenty of open space and minimal wind. Always have a designated launch controller and a clear launch countdown procedure. It is also a good idea to perform a test launch with a smaller engine before using a larger one.

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