We can break this diagonal motion into horizontal and vertical parts; for now, let’s just focus on the former. Let’s say you start with a horizontal velocity (In1) with a value of –1 meter per second and a bounce with a horizontal velocity (In2) +1 m/s. Changing the sign means reversing the direction. Imagine that you are moving back and forth along the x-axis of the coordinate system, negatively to the left, positively to the right.
Notice that your speed remains the same, but speed changes. (Remember that speed has a direction.) In reality, Because Your horizontal velocity reverses, there is a significant boost in speed. (v2 – v1) = (1 – (–1)) = 2. This gives you more impact acceleration, more normal force, and more friction. Bouncing back and forth is key to overcoming gravity in this feat.
How much force would you need to pull off one of those wall-bouncing jumps? Let’s say you have a mass of 165 pounds and a coefficient of friction of 0.6, which is probably conservative for rubber soles.
First, the friction force (FF) must be equal to or greater than the force of gravity (mg). The strength of the gravitational field on Earth (G) is 9.8 newtons per kilogram. So the force of gravity, (mxg) = 75 x 9.8 = 735 newtons.
Remember that the friction force is the normal force times the friction coefficient (FF = μN). To achieve a minimum friction force of 735 Newtons, we need a normal force of at least 1225 Newtons (FF/µ = 735/0.6 = 1.225).
Both of these forces, gravity and the normal force, are pushing down on you, so we need to add them up to get the net force. Since they are perpendicular, we can easily calculate the vector sum as 1,429 newtons. (Heads up, kids: Want to be a parkour hero? Take linear algebra.)
This means you have to push with the same force (since forces are an interaction between two things). 1,429 newtons is 321 pounds of force. This is significant, but not impossible. Doing this eight times in quick successionalthough? Not that uncomplicated.
How much time do you have to turn around? Given the normal force and the mass of the person, we can calculate the horizontal acceleration ANDX. By definition, this is equal to the change in velocity per unit time (Δt), so we can utilize this to solve the time interval:
Plugging in our numbers, we get a time frame of 0.12 seconds. In other words, if you hesitate, you fall. Bottom line is, if you want to pull off this incredible feat of parkour, you need to be powerful, speedy, and fearless—because if you run out of newtons halfway up, the descent is much faster than the ascent.