The important thing is that this is the equation of a parabola. Looking back at the vertical position data from the video, it at least seems fairly parabolic. Even better, the coefficient in front of the t2 term should be the acceleration divided by two. Using the parabolic fit, this gives a vertical acceleration of –11.54 m/s2. True, this is not the expected value of –9.8 m/s2, but it’s really close. (I suspect that my scale for the length of the cannon could be off by a little bit.)
Neither the x nor y-motions of Knoxville disagree with the expected physics. Does it mean the video is real? Nope—it could still be faked, but personally I think that it is indeed real. I mean, doing stupid stunts is the whole point of a movie like this.
How Fast Was He Launched From the Cannon?
Right when Knoxville leaves the cannon, he is moving in both the horizontal (x) and vertical (y) directions. We already know his horizontal velocity, so we would just need the vertical component of velocity.
However, there’s a way to get the total velocity (we call that the magnitude of the velocity vector) just by using the launch angle. Looking at the video and using the protractor tool on Tracker Video Analysis, it seems like the cannon is angled 52 degrees above the horizontal. Since the horizontal and vertical velocities are perpendicular, I can draw the following right triangle:
With this being a right triangle, I can use the cosine as the ratio of the adjacent side (vx) to the hypotenuse (v total). But I know vx and the angle—so, there you go. That puts the total launch velocity at 17.7 m/s (39.6 mph). Yeah, that’s pretty fast. It’s slower than a professionally-pitched baseball, but faster than you can run. This launch velocity will be useful to answer some other questions.
How Far Did He Go?
The trailer doesn’t show Knoxville’s whole motion after being shot from the cannon, but that’s OK. We can use our projectile motion equations to solve for this distance.
The key to any projectile motion problem is that the horizontal and vertical motions are independent, except for the time. That means that I can look at this projectile-human and just consider his vertical position and vertical velocity. I can then use this total time for the horizontal motion and find out where the dude hits the water.