this problem involves a man jumping off a bridge with a bungee chord holding him. he weighs 102 kg and the stretch constant of the chord is 167n/m. And there is a 12N air resistance. the length of the rope when slack is 20 ft what is the minimum height needed for him to do this? my attempt: i had three total attempts which gave me three different answers attempt 1: i divided the problem into three parts, the initial fall till the rope starts to stretch, then the stretch the Ke value that i came up with was mgH, and the sum of the energies is KE-W, which was mg(6.09) -12(6.09). 6.09 m is the length of the chord when it is slack (20ft). the sum of the energies came up to be 6014.484 joules. I then set that equal to 1/2kx^2 12x, which became a quadratic equation: 83.5x^2+12x-6014.484, x being the amount it should stretch, which came up to be about 8.42 meters. The minimum height that i found was 14.51 meters attempt 2: I set mg(height of the bridge)= 0.5kx=(height-the length of chord/rope)^2 which gave me 22.3 m attempt 3: i watched a simulation which showed that when the chord is fully stretched, the kinetic energy during the fall converts to elastic potential and gravitational potential. so, i set the KE = mgx+0.5kx^2, x being the distance it is stretched, and i got 4.4 as the answer for the stretch, and the total height came out to be 10.49m. I do not know which one to use or whether I'm completely wrong. thank you!