I need help one how create a spreadsheet that will give an accurate launch profile for a vertical liftoff for the SpaceX Falcon 9 rocket.

the information they give me is:

•Start with a rocket with a mass, M1, moving with a speed, v1

•The rocket expels some small mass, Δm, with speed, vexhaust

•Treat this as an inelastic collision, and conserve momentum in the process

•Assume the rocket is moving vertically and account for the change in velocity due to gravity

•Compute the velocity of the rocket, v1 + Δv, after taking momentum conservation and gravity into account

•Begin the next step with a rocket with mass, M1 – Δm, and a velocity, v1 + Δv

The spreadsheet need to include the following:

spreadsheet should include at least the following columns:

•Mass of the rocket for that time step

•Change in velocity of the rocket for that time step

•Velocity of the rocket at the end of that time step

•Altitude of the rocket at the end of that time step

Necessary details for the Falcon 9:
Mass at liftoff: 333,400 kg
Fuel/oxidizer used per second: 1430 kg/s
Thrust: 5.01x106 N
Exhaust velocity: 3.50x103 m/s

There are also questions That i need help in answering:

At what time after liftoff does the rocket exceed the speed of sound at STP?
What are its velocity and altitude at this time?
For a vertical liftoff, how long does it take the rocket to reach the edge of space (100 km altitude)?
What other effects do we not consider in this analysis that are important to consider?

To create a spreadsheet that calculates the launch profile for the SpaceX Falcon 9 rocket, you will need to perform calculations based on the given information. Here's a step-by-step guide on how to set up the spreadsheet and calculate the required values:

1. Open a new spreadsheet program (such as Microsoft Excel or Google Sheets).

2. Create column headers for the following parameters: "Time", "Mass of Rocket", "Change in Velocity", "Velocity", and "Altitude".

3. In the "Time" column, start with an initial time value of 0 seconds, and then increment it in small time steps (e.g., 0.1 seconds) for each subsequent row.

4. In the "Mass of Rocket" column, enter the initial mass of the rocket (333,400 kg) in the first row.

5. In the "Change in Velocity" column, you will calculate the change in velocity for each time step. Use the given information that the rocket expels mass (Δm) and the exhaust velocity (vexhaust). Use the formula Δv = (Thrust * Δt) / (M1 - Δm), where Δt is the time step, Thrust is the thrust of the rocket (5.01x10^6 N), and M1 is the mass of the rocket in that time step.

6. In the "Velocity" column, you need to compute the total velocity of the rocket by considering the initial velocity (v1), the change in velocity (Δv), and the effect of gravity. Use the formula v = v1 + Δv - g * Δt, where g is the acceleration due to gravity (9.8 m/s^2). Note that the sign convention should be considered correctly.

7. In the "Altitude" column, calculate the altitude of the rocket for each time step by integrating the velocity values. Start with an initial altitude of 0, and for each subsequent row, add the product of the velocity and the time step.

8. Apply the formulas to the corresponding cells in each column to calculate the values for each time step.

For the specific questions you asked:

1. To determine when the rocket exceeds the speed of sound at standard temperature and pressure (STP), compare the rocket's velocity with the speed of sound (343 m/s). Identify the time step when the velocity exceeds this value and record the corresponding time, velocity, and altitude.

2. To find the time it takes for the rocket to reach an altitude of 100 km, look for the time step when the altitude exceeds 100,000 meters and record the corresponding time, velocity, and altitude.

3. Other effects that are important to consider but not included in this analysis include atmospheric drag, air density variation with altitude, wind resistance, and the Earth's rotation. These factors can significantly affect the rocket's trajectory and behavior during the launch.

Remember to use appropriate formulas, units, and check for any numerical errors.