Slacklining

A slackline is stretched between two trees at a distance, \(d = 10\,\text{m}\), so that a tensioning force, \(F_0 = 5000 \,\text{N}\), is applied on the empty rope. A man then balances in the middle of the rope and exerts a weight force, \(F_g = 750 \,\text{N}\), onto the slackline. What is the vertical deflection, \(h\), of the rope?

Details and Assumptions: The rope is made of an elastic material and obeys Hooke's law \(F = K \frac{l - l_0}{l_0},\) where \(F\) is the force along the rope, \(l_0\) is the initial length, \(l\) is the stretched length of the rope, and \(K = 150\text{ kN}\) is the force constant.