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: $KE=0.5\ast m\ast v^2$, 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: $PE=0.5\ast k\ast x^2$, 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: $0.5\ast m\ast v^2=0.5\ast k\ast x^2$.

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 ：$\boxed{{\displaystyle 2.1}}$ meters is the distance the cord will stretch.