Galileo's Cannon: Proving the Independence of Axes

If you drop a ball from a table and fire another ball horizontally from the exact same height at the exact same instant, which one hits the ground first? Intuition often tells us the dropped ball should win, but physics tells us a different story: they hit the ground simultaneously. Always.

This interactive simulation for Class 11, Class 12, and AP Physics visually proves one of the most counterintuitive yet fundamental concepts in kinematics: the independence of horizontal and vertical motion.

Here is the physics behind what you are seeing:

• The Vertical Axis (y-axis): Once both balls leave the table, gravity is the only force acting on them (assuming no air resistance). Both balls start with an initial vertical velocity of zero (v₀_y = 0). According to the kinematic equation for displacement, Δy = ½gt², the time it takes to fall depends only on the height of the drop (Δy) and gravity (g). Since both share the same height and the same gravity, their fall time (t) is perfectly identical.
• The Horizontal Axis (x-axis): The fired ball has an initial horizontal velocity (v_x). Because there are no forces pushing or pulling it horizontally after launch, this velocity remains perfectly constant. This horizontal speed dictates the range—how far the ball travels sideways (Δx = v_x × t)—but it does absolutely nothing to speed up or slow down the rate of the fall.

Use the controls in this simulation to increase or decrease the horizontal speed of the fired projectile. You will see that whether you launch the cannonball slowly or at blinding speeds, the vertical vectors map perfectly to each other, and both objects strike the floor at the exact same moment.