This page briefly describes how to use the Newton Tool to solve a simple projectile motion problem. In this tutorial we propagate the motion of the system, use the plot tool to generate graphs of interest, and explore how the adaptive step size can effect the results. If you have not already done so, launch the Newton Tool.
Acceleration equations
In order to model a simple projectile motion problem with the Newton Tool, we need to change the parameters in the acceleration panel.
First, since we are dealing with a two dimensional problem we need to change the dimensions to 2. This gives two acceleration equation fields.
We choose x to be the range of the motion and y to be the vertical direction. In the absence of air, the acceleration in the x direction is zero while that in the y direction is -9.81 m/s2. Enter these equations as shown below.
Initial Conditions
Now we need to enter some reasonable initial conditions. For example, enter the initial conditions as shown below:
This will simulate a projectile being hurled from the ground upwards an initial velocity of 30m/s and forwards an initial velocity of 50m/s. Click the Calculate button.
Plots
Flight Distance
After the calculation has finished, click on next. Now make a plot of x vs. y. Leave the axis ranges at their Default values to produce the following graph:
In most cases we won't be interested in values of y below 0, so we can change the parameters to make a more appropriate plot. Change the 'max x-axis value' to 310 and the 'min y-value' to 0:
Now generate the new plot:
From this graph we can see that the projectile soars about 305 meters before hitting the ground.
Flight Time
Change the plot to the below settings to see how long long the projectile is in flight.
This generates the following plot:
It appears the projectile soars for about 6.1 seconds.
Challenge
Can you find a totally different set of initial conditions that has the projectile land around the same spot (305 m)?
