Projectile Motion Simulator

Summary

The tutorial demonstrates how to use a projectile-motion simulator to collect height-versus-time data and model the projectile’s path in Desmos with a quadratic function.

Using the Simulator and Collecting Data

Adjust the cannon’s launch angle, starting height, and initial speed. The example uses a launch angle of about 30°, a starting height of 5 meters, and an initial speed of 15 m/s.

A speed that is too low produces a very short trajectory, while a higher speed provides more useful data. Very high speeds can send the projectile beyond the visible graph. Each plotted dot represents an interval of 0.1 seconds.

Move the simulator’s cursor over a dot to read its exact time and height. The tutorial focuses on height rather than horizontal distance. Enter the time values and corresponding heights in a Desmos table, recording data from launch to just beyond the trajectory’s highest point.

Modeling the Trajectory in Desmos

Graph a quadratic function, (y = ax^2 + bx + c), and adjust the sliders for (a), (b), and (c) until the curve fits the collected data.

• Make (a) negative so the parabola opens downward, as a projectile’s path does.
• Adjust (c) to match the starting height, then tune the other parameters to align the curve with the data points.
• If a slider’s range is too limited, change its minimum, maximum, or step size.

The example’s approximate model is:

[ y = -4.8t^2 + 7.4t + 5 ]

Here, (t) is time in seconds and (y) is the projectile’s height in meters. The fitted curve predicts that the pumpkin will reach the ground a little over two seconds after launch. The simulator’s reading at about 2.03 seconds is consistent with that estimate.

The simulator settings can be changed to explore different launch angles, heights, and speeds, though some trajectories may extend beyond the visible graph.

Speaker and Source

One narrator/instructor demonstrates the projectile-motion simulator and Desmos.