# Two Stage Rocket: Max Height Above Launch Pad

• Toranc3
In summary, the conversation discusses the calculation of the maximum height reached by a two-stage rocket launched from rest with a constant acceleration and then boosted by a second stage. The equations y=yo + vo*t +1/2*a*t^(2) and vy=vo + a*t are used to calculate the height and velocity of the first stage, and the final velocity of the first stage is found to be 87.5m/s. The second stage is then boosted to a final velocity of 132.5m/s and a new acceleration of 4.5m/s^(2) is used to calculate the final height of 2193.75m. However, it is noted that this is not the final height of the rocket
Toranc3

## Homework Statement

In the first stage of a two-stage rocket, the rocket is fired from the launch pad starting from rest but with a constant acceleration of 3.50 m/s^2 upward. At 25.0 seconds after launch, the second stage fires for 10 seconds, which boosts the rocket's velocity to 132.5m/s upward at 35 seconds after launch. This firing uses up all the fuel, however, so after the second stage has finished firing, the only force acting on the rocket is gravity. Air resistance is negligible.

A) Find the maximum height that the stage two rocket reaches above the launch pad.

## Homework Equations

y=yo + vo*t +1/2*a*t^(2)

vy=vo + a*t

## The Attempt at a Solution

First stage:
y=yo + vo*t +1/2*a*t^(2)
y=1/2(3.5m/s^(2))*(25s)^(2)
y=1093.75m

Vy=Vo + a*t
Vy=3.50m/s^(2)*25s= 87.5m/s
Final velocity of first stage=87.5m/s

Second Stage:
Initial velocity of second stage=87.5m/s
vy=vo+a*t
132.5m/s=87.5m/s +a*10sec
a=4.5m/s^(2)

New acceleration=4.5m/s^(2)

y=yo + vo*t +1/2*a*t^(2)

y=1093.75m + 87.5m/s*10s + 1/2(4.5m/s^(2))*100s= 2193.75m

Is this the correct answer? Thanks!

Yes, it looks right. It would have been slightly simpler to compute the stage two height delta by average velocity: 2s = (v0+vf)t
I assume there are more parts to the question.

haruspex said:
Yes, it looks right. It would have been slightly simpler to compute the stage two height delta by average velocity: 2s = (v0+vf)t
I assume there are more parts to the question.

Thanks and yes there are more parts to this question. I am going to work on them and then post them back on here.

2193.75m is the height after the second stage finished firing - but the rocket still has a velocity upwards, and will continue to increase its height afterwards.

Your solution looks correct! To double check, we can also use the kinematic equation for displacement without time, y= yo + 1/2* a*t^2, since we know the initial and final velocities and acceleration for the second stage. This would give us the same answer of 2193.75m. Great job on solving this problem!

## 1. How does a two stage rocket work?

A two stage rocket is composed of two sections, or stages. The first stage contains the majority of the rocket's engines and is responsible for launching the rocket off the launch pad and into the air. Once the first stage's engines have burned all their fuel, it separates from the rocket and falls back to Earth. The second stage then ignites its engines and continues to propel the rocket higher into the atmosphere.

## 2. What is the purpose of using a two stage rocket?

A two stage rocket allows for greater distance and height to be achieved compared to a single stage rocket. By having two stages, the rocket is able to conserve fuel and weight by shedding the first stage once it has expended its fuel. This allows the second stage to have a lighter load and thus achieve greater heights.

## 3. How high can a two stage rocket go?

The maximum height a two stage rocket can reach above the launch pad depends on various factors such as the weight and design of the rocket, the amount of fuel it carries, and the thrust of its engines. However, two stage rockets have been known to reach heights of over 100 miles above the Earth's surface.

## 4. What happens to the first stage after it separates from the rocket?

After the first stage has burned all its fuel and separated from the rocket, it falls back to Earth and usually disintegrates upon re-entry into the atmosphere. Sometimes, the first stage may be equipped with parachutes to slow its descent and allow for a controlled landing.

## 5. Are there any disadvantages to using a two stage rocket?

One potential disadvantage of a two stage rocket is the added complexity and cost of designing and building a multi-stage rocket compared to a single stage rocket. Additionally, the separation and ignition of the second stage must be timed perfectly for the rocket to reach its intended trajectory and height.

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