Physics of Fitness Fridays - Jump Around!

1. Today we’re going to look at the physics of jumping. What happens when you jump straight up in the air?

1. Typically in a vertical jump you will bend your knees and swing your arms back, then jump up into the air before you land back on the ground.

1. Today we are going to look at the airborne part of the jump to ask the following question: what determines how high you will go? To keep things, simple, we’re going to determine the height above a reference point—here, the reference point will be the height of your COM just as your feet are leaving the ground (designated by the yellow line).

1. When jumping your body has energy. That energy takes two forms: the first is kinetic energy (KE) and is determined by your upward velocity v. KE is given by the equation KE = (1/2) mv^2, where m is your mass and v is your velocity. You also have potential energy PE. This is determined by your height above the reference point h. Potential energy is given by PE = mgh, where m is-again—your mass, h is your height above reference, and g is the acceleration of gravity. At every point in a jump, you have a combination of kinetic and potential energy.

1. Now we’re going to look at the two most important points of the jump; right when you takeoff and at the top of the jump. When you take off, your potential energy is zero because we said that your height at this point is the reference point, or h = 0. Your kinetic energy, however, is based on your velocity and is given by the KE equation.

At the top of the jump, your velocity is zero. (Think about it; at the top of your jump you switch from lifting up to lowering down, so there must be a moment when you are not moving, that is, you’re “turning around”.) So, you have no kinetic energy, but your potential energy is given by PE = mgh.

1. The conservation of energy states that the total energy throughout the jump is constant. So if we set the total energy at takeoff equal to the total energy at the top of the jump, we get (1/2) mv^2 = mgh. Solving for height gives h = (v^2)/2g. So the more speed you have at takeoff, the higher you will go.

1. So how do you increase takeoff speed? I’ll give you the short answer, which is that the more force you exert as you squat down and then extend your legs, the more acceleration you will have. And the more you accelerate as you “prep” for the jump, the more your velocity will be at takeoff. The mechanics of what is actually going on though is a bit complicated, so I will save that for another time. In the meantime, let’s see your best jump!