# Rocket Performance Homework: Max Velocity & Altitude

• Theboob651
In summary, the teacher made a mistake in his equations. He forgot to include the propellant mass into the total initial mass. This caused him to have a different average mass for the thrust and coast phases, resulting in the same final velocity and altitude.
Theboob651

## Homework Statement

I need to find out the rockets max velocity and max altitude. My teacher gave us an example but everytime i use the stuff we know his answer doesn't match mine.
So we know: Rockets mass=23 grams
mass of engine=16.2 grams
mass of propellant=3.12
average thrust=8 Newtons
burn duration=.5 seconds
His max velocity=101.37
His max altitude=549.621

## Homework Equations

The equations he gave us are:
x = Xo + vt, v=Vo +at, x = Xo+Vot+.5at^2, and f=ma

x=distance, v=velocity, t=time, a=acceleration, f=force

## The Attempt at a Solution

Whenever i plug all the stuff in i come up with a Max velocity of 102.04
Then i really don't know where to go from there to even check his altitude.
thanks

Last edited:

Your initial mass is Mass of Rocket + Mass of Engine + Mass of propellent
Your mass is not constant. It decreases from initial mass to initial mass minus propellent mass. So find your average mass and use that for mass in the formulas you give. Your teacher's velocity of 101.37 is what I get if I forget to include propellant mass into total initial mass. I get a velocity in the low 90s if I remember to include it. I'll let you figure out the exact number.

Your average acceleration is given in your final formula, rewriting f=ma as a=f/m, where m is your average mass. That's your upward acceleration from the rocket's thrust. Your total acceleration will be this minus gravity. Your 2nd equation is v=at (since Vo is 0). Use it once you have your average acceleration.

For height, you need to break it up into two problems: 1 while the rocket is thrusting you use your average acceleration computed earlier, and 1 while the rocket is coasting to its maximum height, where acceleration will simply be 9.8 m/s down.

the initial mass is the rocket mass plus the engine mass, the propellant mass is included in the engine mass. the propellant mass is used to find the mass of the coasting rocket. thanks though. if you have any other ideas please help

If that's the case then I get the same answer as your teacher. During the thrust phase, your mass begins as (rocket mass + engine mass) and ends as (rocket mass + engine mass - propellant mass). So your average mass will be halfway inbetween these values. Acceleration due to thrust = F/m, where F is 8 N, and m is the average mass you just computed. Subtract from this acceleration the acceleration due to gravity. Then use your kinematics formula and you'll get 101.369926 m/s, same as the teacher's rounded number.

Thanks

## 1. What is the purpose of calculating the max velocity and altitude of a rocket?

The purpose of calculating the max velocity and altitude of a rocket is to determine the performance and capabilities of the rocket. This information is important for designing and testing rockets for specific missions, as well as for ensuring safe and efficient flight.

## 2. How is the max velocity of a rocket calculated?

The max velocity of a rocket is calculated using the rocket equation, which takes into account the mass of the rocket, the mass of the propellant, and the specific impulse of the engine. This equation can also be used to calculate the delta-v or change in velocity of the rocket.

## 3. What factors can affect the max altitude of a rocket?

The max altitude of a rocket can be affected by several factors, including the thrust of the rocket engine, the aerodynamics of the rocket, the weight of the rocket and its payload, and external factors such as air resistance and wind speed. The efficiency of the rocket's engine and the amount of propellant also play a role in determining the max altitude.

## 4. How does air resistance impact rocket performance?

Air resistance, also known as drag, can significantly impact the performance of a rocket. As the rocket travels through the atmosphere, it experiences resistance from the air, which can decrease its speed and altitude. This is why rockets are designed with streamlined shapes and often use fins to reduce drag and improve performance.

## 5. Can the max velocity and altitude of a rocket be accurately predicted?

The max velocity and altitude of a rocket can be accurately predicted using mathematical equations and computer simulations, but there are many variables that can affect the actual performance of a rocket. Factors such as weather conditions, engine malfunctions, and human error can all impact the final results. Therefore, these calculations are used as estimates and can be refined through testing and analysis of actual rocket flights.

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