The important thing is that this is the equation of a parabola. Looking at the video’s vertical position data, it at least looks quite parabolic. Better yet, the coefficient in front of the t2 term must be the acceleration divided by two. Using the parabolic fit this gives a vertical acceleration of –11.54 m / s2. It’s true, it’s not the expected value of –9.8 m / s2, but it’s really close. (I suspect my scale for barrel length might be off slightly.)
Neither the x motions nor the y motions of Knoxville disagree with the expected physics. Does this mean the video is real? No it could Again be rigged, but personally I think it’s real. I mean, doing silly stunts is the whole point of a movie like this.
How fast was it launched from the cannon?
Just as Knoxville leaves the cannon, it is moving in both the horizontal (x) and vertical (y) directions. We already know its horizontal speed, so we would only need the vertical component of the speed.
However, there is a way to get the total velocity (we call this the magnitude of the velocity vector) just by using the launch angle. Watching the video and using the protractor tool on Tracker Video Analysis, it appears that the barrel is tilted 52 degrees above horizontal. As the horizontal and vertical speeds are perpendicular, I can draw the following right triangle:
This being a right triangle, I can use the cosine as the ratio of the adjacent side (vX) to the hypotenuse (total v). But I know vX and the angle, so there you go. This puts the total launch speed at 17.7 m / s (39.6 mph). Yeah, it’s pretty quick. It’s slower than a professional baseball, but faster than you can run. This launch speed will be useful for answering other questions.
How far has he gone?
The trailer doesn’t show all of Knoxville’s movement after being shot down by the cannon, but that’s okay. We can use our projectile motion equations to solve this distance.
The key to any projectile motion problem is that horizontal and vertical motions are independent except for time. This means that I can look at this human-projectile and just consider its vertical position and vertical velocity. I can then use that total time for the horizontal movement and find out where the guy is touching the water.