321 point Watching a video of a bungee jumper, you decide to do some physics! You look up the spring constant of the bungee cord and find that it is $65,000 \mathrm{~N} / \mathrm{m}$. How far will the cord stretch if the jumper has a mass of $65 \mathrm{~kg}$ and has a velocity of $66.2 \mathrm{~m} / \mathrm{s}$ right before the cord starts to stretch? Round to one decimal place.

Step 1 ：Calculate the initial kinetic energy (KE) using the formula: \(KE = 0.5 * m * v^2\), where m is the mass of the jumper (65 kg) and v is the velocity (66.2 m/s).

Step 2 ：Calculate the potential energy (PE) stored in the stretched bungee cord using the formula: \(PE = 0.5 * k * x^2\), where k is the spring constant (65,000 N/m) and x is the distance the cord stretches.

Step 3 ：Set the two equations equal to each other and solve for x: \(0.5 * m * v^2 = 0.5 * k * x^2\).

Step 4 ：Plug in the values and solve for x: \(m = 65\), \(v = 66.2\), and \(k = 65,000\).

Step 5 ：Calculate the final answer: \(x = 2.1\) meters.

Step 6 ：\(\boxed{2.1}\) meters is the distance the cord will stretch.