freefall position kinematic equation feet

The equation for conservation of energy is given as follows: Since friction and air resistance are neglected, the only force that does work on the system is gravity. This will allow us to determine the velocity v of the jumper as a function of y. Since friction and air resistance are neglected, the physics occurring between positions (1) and (2) can be analyzed using conservation of energy for the system, which consists of bungee jumper and bungee cord. By geometry, the vertical velocity of the bottom tip of the bend is v/2, and the vertical acceleration of the bottom tip of the bend is a/2. The vertical velocity of the jumper is given as v, and the vertical acceleration is given as a. The lengths of the straight sections of the cord are given as a function of y, and are based on the geometry of the problem. The position of jumper and cord is set as a function of y which is the position of the jumper M relative to the datum (chosen as his original vertical position). The following schematic for this analysis shows a representation of the bungee jumper and bungee cord after he jumps. This is equation (1) in the analysis given below. This means that the change in elastic potential energy of the hanging part of the bungee cord (the left side of the cord in the two figures below) is small enough to be neglected in the conservation of energy equation. During the initial part of the fall, the extra stretching that occurs in the hanging part of the bungee cord as it supports more of its own weight, is negligible.Thus, the length of the bungee cord is approximately L. The radius R of the bend is small relative to the length of the straight sections of the bungee cord.Friction and air resistance can be neglected.The jumper M falls vertically downward during the fall, and the falling part of the bungee cord remains directly below him during the initial part of the fall where the bungee cord is slack.The sign convention is 'up' as positive and 'down' as negative.Īdditional assumptions in this analysis are: The acceleration due to gravity is g (equal to 9.8 m/s 2 on earth). The left side of the bungee cord is attached to a fixed support.

The bungee cord is represented by two lengths of rope, each with length L/2, with a bend at the bottom of radius R. The jumper is represented as a point object of mass M. The following schematic for this analysis shows a simplified representation of a bungee jumper and bungee cord, at the initial position (1), before he jumps. The physics taking place here will be examined next. This takes place in the initial part of the fall while the bungee cord is slack (i.e. However, what is particularly interesting in the following analysis of the physics of bungee jumping is that the jumper experiences a downward acceleration that exceeds free-fall acceleration due to gravity. The jumper then oscillates up and down until all the energy is dissipated. The bungee jumper jumps off a tall structure such as a bridge or crane and then falls vertically downward until the elastic bungee cord slows his descent to a stop, before pulling him back up.

The basic physics behind this activity is self-evident. The physics of bungee jumping is an interesting subject of analysis.

Freefall position kinematic equation feet