# How to Calculate the Flight Time and Apex for a Model Rocket Launch in Excel?

In summary: Is there a way to account for the acceleration? In summary, the rocket has a speed of 46.53 m/s and an altitude of 121.58 m at the end of the flight.
A brief explanation, this assignment is to be done in Excel and also has to be turned in with handwritten solutions for finding total flight time and apex. If I can get the handwritten part done Excel is a piece of cake.

## Homework Statement

A model rocket is launched and I am to evaluate the 3 stages it goes through. During the first 0.15s the rocket (m=0.05 kg) is launched with a force of 16N. It then coasts upward while being slowed done by gravity (g=9.81m/s2. After it reaches apex(max altitude it starts to fall back down. It also deploys a parachute 6 sec. after the motor stops with a constant speed of 10 m/s until it hits ground. Calculate the speed and altitude of the rocket over it's flight time and plot them.

Knowns:
g=9.81m/s2
FE=16N
m=0.05 kg
vo=0m/s
$$\Delta$$t=0.01s

Unknowns:
acceleration
velocity
height
total time

## Homework Equations

$$\Sigma$$F=ma
v(t)=vo+at
h(t)=ho+vo+.5at2

## The Attempt at a Solution

Stage 1: 0$$\leq$$ t $$\leq$$ 0.15s
use dt=0.01s (was told to do this by teacher for stage 1)
$$\Sigma$$F=ma
Fe-w=may
ay=$$\frac{Fe-w}{m}$$
ay=$$\frac{16N-(0.05)(9.81)}{0.05}$$=310.19m/s2

v=vo+at
v=0+(310.19)(0.15)=46.53m/s

h=ho+v0+.5at2
h=.5at2
h=.5(310.19)(0.15)2
h=10.47 m

Stage 2: 0.15 $$\leq$$ t $$\leq$$ 6.15s
$$\Sigma$$F=ma
-w=may
ay=-g

v=vo+at
v=46.53+(9.81)(6.15)=106.86m/s

h=10.47m+(46.53)(6.15)+.5(-9.81)(6.15)2=111.11m

Stage 3: 6.15 $$\leq$$ t $$\leq$$ total time

Stage 3 is were I get lost could some point me in the right direction as to find total time and apex.

Your stage 2 is incorrect. At the end of stage 1, you have the rocket's velocity as 46.53 m/s upwards (correct). Then at the end of stage 2, during which the only force is gravity (downward), you have the rocket's velocity as 106.86 m/s upwards. Ask yourself, does this make any sense?

So I would be using -9.81 instead of 9.81 for gravity now? Also would apex be the addition of the height of stage 1 & 2 added together. 111.11 + 10.47 = 121.58m?

Also the velocity and height numbers seem small given the acceleration at lift off.

Last edited:

## 1. How does a rocket launch in 3 stages?

A rocket launch in 3 stages is a process where the rocket is divided into three main parts, each designed to function during different phases of the launch. The first stage is responsible for the initial liftoff and uses the most powerful engines to generate enough thrust to overcome the Earth's gravity. Once the first stage has burned all of its fuel, it separates from the rocket and falls back to Earth. The second stage then ignites and continues to propel the rocket into higher altitudes. Finally, the third stage, also known as the upper stage, takes over and delivers the payload to its desired orbit.

## 2. Why is a 3-stage rocket used instead of a single-stage rocket?

A 3-stage rocket is used because it allows for a more efficient use of fuel and greater payload capacity. By having multiple stages, the rocket can shed the weight of empty fuel tanks and engines as it ascends. This reduces the amount of fuel needed for the entire launch and allows for a larger payload to be carried. A single-stage rocket would require significantly more fuel and would not be able to reach the same altitude or carry as much weight.

## 3. What is the purpose of the upper stage in a 3-stage rocket launch?

The upper stage in a 3-stage rocket launch is responsible for delivering the payload, such as a satellite, into its desired orbit. This stage typically uses a different type of engine that is more efficient in the vacuum of space. It also has a smaller size and weight compared to the first and second stages, allowing for a more precise and controlled delivery of the payload.

## 4. How is the separation of stages controlled during a 3-stage rocket launch?

The separation of stages is controlled through a combination of mechanical and pyrotechnic systems. The first and second stages are typically connected by a series of bolts and clamps, which are released using pyrotechnic charges at the appropriate time. The third stage is usually connected using a more delicate system, such as springs or small explosive charges, to ensure a smooth separation without damaging the payload.

## 5. Has a 3-stage rocket always been used for space launches?

No, a 3-stage rocket has not always been used for space launches. In the early days of space exploration, single-stage rockets were used due to technological limitations. As technology advanced and the need for larger payloads and farther destinations arose, the use of multi-stage rockets became necessary. The first 3-stage rocket was used in 1961 for the launch of the Vostok spacecraft, and since then, it has become the standard for most space launches.

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