# Projectile Motion: Initial Velocity Derivation

• PhysicsIBStudent
In summary, the speaker is working on a school project involving water rockets and is struggling to produce an accurate mathematical model. They have compared their model's results to a water rocket simulator, but they are very different. They have also questioned the accuracy of their initial speed calculation and have requested a PDF version of their attached file. The speaker clarifies that their equation for determining range only applies to non-zero launch angles.
PhysicsIBStudent
Hey guys, I am working on a school project and have fired some water rockets at different angles. I am now trying to compare theoretical results vs experimental results. But I am struggling to produce an accurate mathematical model.

I have attached my attempt to this post. It is quite long and possibly overly complex. I have not taken drag into account for this model.

I have compared the range results I got from my model to some from a water rocket simulator which was fed the same initial conditions but they are very different.

My question is whether my model is anywhere close to correct or where I went wrong. I used data from my water rocket to attempt to find the initial velocity of the rocket. I don't think my initial speed is correct tho.

#### Attachments

• Initial velocity.pdf
239.1 KB · Views: 477

berkeman said:

Done. Please let me know if there are issues opening the pdf

Equation (12) is suspicious. According to (12) what is the range when the projectile is launched horizontally (θ = 0)?

Tom.G said:
Equation (12) is suspicious. According to (12) what is the range when the projectile is launched horizontally (θ = 0)?

Your right I forgot to mention this equation assumes you are launching from ground-level and the ground is flat. The formula only intends to work for non zero angles as launching at 0 degrees would result in a crash of some sort.

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the force of gravity. It follows a curved path due to the constant downward acceleration of gravity.

## 2. How is initial velocity derived in projectile motion?

The initial velocity in projectile motion is derived using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time. By rearranging this equation, we can solve for the initial velocity, u = v - at.

## 3. What is the formula for calculating the range of a projectile?

The formula for calculating the range of a projectile is R = (u^2 * sin(2θ)) / g, where R is the range, u is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. This equation assumes that the initial height of the object is equal to the final height.

## 4. How does initial velocity affect the trajectory of a projectile?

The initial velocity has a direct impact on the trajectory of a projectile. A higher initial velocity will result in a longer range and a flatter trajectory, while a lower initial velocity will result in a shorter range and a steeper trajectory.

## 5. What are the other factors that can affect the trajectory of a projectile?

Aside from initial velocity, other factors that can affect the trajectory of a projectile include the angle of projection, air resistance, and the initial height of the object. These factors can alter the range and shape of the projectile's trajectory.

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