How’s Your Throwing Arm? Do the Math




Every summer, the various PTC office locations hold a PTC Family Day in which PTC employees can bring family members to the office for a day of fun, games, and food. For the last three summers, the Mathcad team at HQ has hosted the Mathcad Rocket Toss. I guess I’m a little biased, but I think it’s the most popular activity of Family Day.

Kids tossed a PTC Rocket in the air, while application engineers calculated its trajectory with Mathcad.


Last Friday was PTC Family 2016, and we had somewhere around 125 kids and adults participate in the Rocket Toss. It was a lot of fun, albeit extremely hot. I tried to stay in the shade, but the sun kept chasing me down (funny how that works).

How it works

The child (or adult; we don’t discriminate) writes her name and height on a piece of paper. Then she stands at a designated location and launches the rocket with all her might. We have someone using a stopwatch to determine the time the rocket is in the air, as well as someone tracking the landing and giving a horizontal distance of the rocket.

In Mathcad (PTC’s math software for engineers), we enter the person’s height, typing in feet-inches format within a string and then using the FIF unit, which processes that string into a length.

FIF equation

We also enter the hang time and horizontal distance of the rocket. Using these three pieces of information, we use basic kinematic equations to determine the height of the rocket’s trajectory as well as the initial speed of the rocket. Currently we do not account for air resistance.

Rocket calculation worksheet


Each year, we have made some additions to this. The worksheet shown above is what we used the first year of the Rocket Toss.

Last year, we added a plot of the trajectory. But that only shows a parabola. For a kid, it’s not easy to figure out what the plot actually means. So we calculated (using that quintessential high school trigonometry problem using shadows) the height of the flag pole in the front of PTC HQ and added that to the plot to give a sense of scale.

Projectile path with flagpole

With that addition, participants could visualize the trajectory of their throw. This year, we stepped it up a notch and allowed participants to see an instant replay.

Setting up a variable t to be a variable for iteration, we launch the worksheet using the Animator Tool (available in Mathcad subscription bundle packages). For the Stop value, we use the hang time of the rocket.

Animation window

Then we press play, allowing us to see how the rocket actually traces its own trajectory in time. I don’t want to brag, but the kids thought that was pretty cool. Like I said, we have the best activity at PTC Family Day ;)

Beyond Spreadsheets and Calculators

Did you know you can download the same software used in this story free? Engineers use Mathcad for everything from designing new musical instruments to teaching nuclear medicine. Download yours today.

Download Mathcad Express

Featured image cropped from “Fastball” by John McStravic, via Flickr