# Trajectory Modeling

This is an example of how to model the simple trajectory of a potato discharged from a potato cannon. To do this you need to have the gravitational constant, velocity of the projectile as it leaves the barrel, and the angle between the barrel and the ground.

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## Step 1: Finding Velocity

My first step is to find the velocity. I used the method of finding the distanced traveled per frames. Knowing the frame rate of the camera, the velocity can be calculated. In my case I calculated, as seen in the video, the velocity to be 60ft/s since it traveled 5ft in 5 frames while being filmed at 60 frames/s.

5ft * (1/5 frames) * 60 frames/s = 60ft/s

## Step 2: Velocity in X and Y directions

Now we find the velocity in the X and Y directions. For the X direction,

Vx = Vcos(angle) = 60cos(30) = 51.96ft/s

And the Y direction

Vy = Vsin(angle) = 60sin(30) = 30.00ft/s

## Step 3: Plug and Chug

Now we have:

Vx = 51.96ft/s

Vy = 30.00ft/s

g = -32.2ft/s^2 (gravitational constant)

y0 = 4ft (Height of end of the barrel above the ground)

Now we plug them into the trajectory formulas:

x(t) = (a*t^2)/2 + Vx*t + x0

y(t) = (g*t^2)/2 + Vy*t + y0

We know that there is no horizontal acceleration (a = 0) and we are starting at x0 = 0

So plugging in Vx, Vy, y0 and g gives us,

x(t) = 51.96t

y(t) = -16.1t^2 + 30t + 4

jakeframe7 months ago

You could take this experiment a step further by measuring the real world trajectory and using that data to calculate the air resistance.

showden (author)  jakeframe7 months ago

I actually started out doing that and creating my own drag coefficient model. But it got into differential equations with conflicting x and y equations. I think I messed up with the integration so I simplified it and didn't worry about the drag, haha. But I had it narrowed down to two equations and two unknowns after putting in the initial conditions, but something was off.

Migs7 months ago