A bungee jumper of mass 75 kg is standing on a platform 53 m above a river. The length of the unstretched bungee cord is 19 m. The spring constant of the cord is 65.5 N/m. Calculate the jumper's speed at 11 m below the bridge on the first fall.

 

I suspect there is more to this question, because this first part does not make use of the bungee chord. The chord starts stretching after the jumper passes 19 meter below the bridge mark, but here we are asked to find the speed below just 11 meters.

To that end, we are going to neglect air resistance and use energy method.

Potential energy before the jump (with respect to 11 m below the bridge) = kinetic energy at 11 m below the bridge ==>

(75 kg)·(9.8 m/s²)·(11 m) = ½·(75 kg)·v² ==> v² = 215.6 ==> v = 14.68 m/s