Use parametric equations to model the flight of a baseball.
Two functions — x(t) for horizontal distance and y(t) for height —
share the hidden variable t (time in seconds) to trace the ball's path.
Choose a ballpark, then see if physics delivers a home run!
Select a park to explore:
🏟️
Progressive Field
Cleveland, OH
🟩
Fenway Park
Boston, MA
🧱
Wrigley Field
Chicago, IL
Will It Clear the Wall?by Claude, prompts by Mr. C. · Parametric Equations & Baseball
Most textbook graphs of projectile motion use different scales on the
horizontal and vertical axes — stretching the vertical to make the arc look tall
and dramatic. That's fine for showing shape, but it distorts angles.
On this graph, 1 foot horizontal = 1 foot vertical.
The angle you see at launch is the true launch angle.
Try this: set the launch angle slider to 45°. On an equal-scale graph the
ball's initial direction should bisect the right angle between the axes exactly —
and you can verify it with a protractor on screen.
At shallow angles (10°–15°) the arc will look nearly flat — because it
really is nearly flat. That's honest geometry, not a display problem.
Most graphing calculators and simulation tools use unequal scales by default.
Always check the axis tick marks before reading an angle off any graph.