Video Analysis of a Howitzer Cart — A Fun Projectile Motion Demo
It’s often called a Howitzer cart. In this physics demo, a cart rolls with a constant speed on a horizontal track. At some point, a ball is launched straight up into the air. The fun part is that the ball lands right back in the cart. Here, check it out.
Why does this work? Well, let’s start with an equation of motion for the cart. Since it’s on a horizontal track moving with a constant velocity, it’s position can be described as the following kinematic equation.
Here x_c is the position (as a function of time), x_c0 is the position at time t = 0 and v_c is the velocity. What about the ball? If it is launched vertically (with respect to the cart) then it has the same horizontal velocity as the cart. While in the air, the only force is the downward gravitational force — but the horizontal velocity remains constant.
With that, we have the following two kinematic equations for the motion of the ball (it’s just a projectile).
