This page discusses how to use the Newton Tool to simulate a projectile motion problem with air resistance present. If you've gone through the previous Projectile Motion Tutorial, this example will just be a simple modification. If you have not already done so, launch the Newton Tool.
Acceleration Equations
Just like in the previous tutorial, enter 2 in the 'Dimensions' field. The equations we enter will include air resistance 'drag' terms:
The '0.1' terms in front of vy and vx correspond to how strongly the projectile is affected by the air resistance. For example, if you want to see what happens if you model a less aerodynamic projectile change the 0.1 values to 0.3 and see how the graphs change.
Initial Conditions
For this tutorial, use the same initial conditions as we used in the first Projectile Motion tutorial.
Plots
Run the calculation and then generate an x vs. y plot with the y axis minimum at 0:
If we compare where this graph crosses y=0 to where it did in the first Projectile Motion tutorial, we see it hits about 212 m down range compared to 305 m in the case without air resistance.
Now, go back to the 'Plot Results' panel and select 'x velocity' under 'plot on y-axis', and 'time' under 'plot on x-axis'. Also, type 'Default' into the 'min y-axis value' field. This plot illustrates that the velocity in the x direction is decreasing due to the air resistance we introduced.
In the absence of air resistance, the x velocity would be constant in time.
Challenge
How might you change the acceleration equations to reflect a constant wind blowing in the x direction? Is it possible to choose a wind that will cancel out the air resistance term we included, even though the air resistance term depends on vx?
