If you are afraid of heights, this is a super scary video. In case you are too afraid to watch it, this dude jumps off the top of a building that is listed at 129 feet and lands in water. But wait! Although that's crazy, the crazy part is that he jumps over two docks in order to hit the water (and not the wooden dock).

The physics question here is: How hard is it to jump over that second dock?

Human Projectile Motion

When you have an object whose motion is only determined by the gravitational force, that's called projectile motion. So, to be clear, that's the time right after the dude leaves the building until right before he hits the water. If this is true projectile motion, there would have to be negligible air resistance—which I will assume for now.

Actually, this is a great example of projectile motion since it appears that the guy launches horizontally off the building. Let me start with a diagram and some parameters that I will need to estimate.

Of course this isn't a very accurate diagram—you can tell because the jumper didn't actually scream "AHHHHHHH." But anyway, I can still analyze the motion. There is one key element to projectile motion—and it is this: You can treat the horizontal motion (x-direction) and the vertical motion (y-direction) as two separate one-dimensional kinematics problem. The only thing these two 1D motions share is time. The time it take the guy to move in the x-direction is the same time it takes him to move in the y-direction.

Let's look at this y-motion first. Since there is only the gravitational force pulling down, the dude will have a vertical acceleration of negative g (where g = 9.8 N/kg or 9.8 m/s2). If I call the water level the location where y = 0 meters, then he starts at a y-value of h with an initial y-velocity of 0 m/s (since he jumped horizontal and not up).

With this, I can use the following kinematic equation (for motion with a constant acceleration):

If you want to know where this equation comes from, I can recommend this excellent book on introductory physics. Or if you prefer a more hands-on approach, here is my incomplete online book for introductory physics using Python. But using this equation I can put in my values for the starting and ending y-position as well as the initial y-velocity and solve for the time.

This expression for time can be used in the x-motion. Since there are no horizontal forces on this dude, the x-acceleration is zero. This means there is just the following (and simpler) kinematic equation.

I will set the starting x-value to zero and the initial x-velocity is just the dude's launch velocity (the magnitude of initial velocity vector).

Substituting the expression for time, the horizontal distance traveled will be:

Let's take a moment to just check this equation.

Does it have the correct units? The left side of the equation is in meters, what about the right? (hint: yes)

What if you jump from a higher distance? Will you go farther horizontally? Should you? (yes to both)

What if you launch with a greater velocity? Will you go farther? Again yes.

What if you are on a planet with zero mass and g = 0 N/kg? What does this equation say will happen and what should happen? I'm not answering this one for you, sorry.

OK. Now we can use this expression to look at the jumping guy. Oh, this is essentially the same experiment you did in your introductory physics lab. No, you didn't jump off a building like a crazy person. Instead, you probably had one of these ball launchers that shot a small metal ball horizontally off a table and onto the floor. Replace the ball with a crazy person and you get 1 million views on Youtube.

Actual Jumping Guy

OK, what do we know? The video says this is in Newport Harbor—but I think it's Newport Beach harbor. Pretty sure this is the location from Google Maps.

The great thing about Google Maps is that I can use it to find the horizontal jump distance. I get a value of approximately 7.4 meters. If I assume the height is correct (at 129 feet or 39.3 meters), I can use these two values to calculate this crazy dude's launch speed.

A launch speed of around 2.6 m/s is like a slow jog or fast walk (it's a jalk)—but definitely seems like a reasonable starting speed. The guy easily could have taken a running start to get a faster speed, but he didn't. Really, I'm wondering if he was trying to land in between the two docks. If that's the case, he was probably freaking out a little bit on the way down thinking that he might hit that second dock. Or maybe he was thinking of how many Youtube views he was going to get.

But there are still some questions. I will leave these for your homework assignment.