Physics of Johnny Knoxville, Human Cannonball

The important thing is that this is a parabolic equation. Looking back at the vertical position data in the video, it at least looks pretty parabolic.Even better, the coefficient before t² The term should be acceleration divided by two.Using a parabola fitting, this gives a vertical acceleration of –11.54 m/s². That’s right, this is no –9.8 m/s expected value²But it’s really close. (I suspect that my cannon length ratio may deviate a bit.)

Both the x and y motions in Knoxville are inconsistent with the expected physical phenomena. Does this mean that the video is real?No-it can still It is a fake, but I personally think it is indeed real. I mean, doing stupid stunts is the whole point of such a movie.

How fast does he fire from the cannon?

Just as Knoxville left the cannon, he was moving in the horizontal (x) and vertical (y) directions. We already know his horizontal velocity, so we only need the vertical component of the velocity.

However, there is a way to get the total velocity (we call it the magnitude of the velocity vector) by using the launch angle. Viewing the video and using the protractor tool on Tracker Video Analysis, the cannon appears to be at a 52 degree angle to the horizontal. Since the horizontal and vertical speeds are vertical, I can draw the following right triangles:

Since this is a right triangle, I can use cosine as the adjacent side (v_X) To the hypotenuse (v total). But i know v_X And the angle-so there you go. This gives a total launch speed of 17.7 m/s (39.6 mph). Yes, this is pretty fast. It is slower than professional baseball games, but runs faster than you. This launch speed will help answer some other questions.

How far has he gone?

The trailer didn’t show the whole action after Knoxville was hit by a cannon, but it was okay. We can use our projectile motion equation to solve for this distance.

The key to any projectile motion problem is that horizontal and vertical motion are independent, except for time. This means that I can look at this projectile human, considering only his vertical position and vertical speed. Then I can use this total time for horizontal movement and find out where the guy hit the water.