A Bungee Jumper's Surprise

📌 CONCEPT: The potential energy stored in a stretched bungee cord is converted into kinetic energy of the jumper as it stretches and releases, allowing the jumper to gain speed before hitting the water.

📐 RULE / FORMULA: The conservation of energy principle is used to solve this problem, where the initial potential energy equals the final kinetic energy, given by PE = mgh = (1/2)mv^2.

💡 WORKED EXAMPLE: Let's assume Rahul's mass is 60 kg. Initially, he is 200 m above the ground, and the bungee cord stretches by 50 m before releasing all stored energy. By the time he reaches 20 m above the ground, the bungee cord has already released its energy. Using PE = (1/2)mv^2, we can calculate the speed v. First, find the potential energy at 200 m: PE = 60 kg * 9.8 m/s^2 * 180 m = 105,120 J. Then, equate this to the final kinetic energy: 105,120 J = (1/2) * 60 kg * v^2. Solve for v to get v = √(105,120 J / 30 kg) = 32.1 m/s.

⚠️ COMMON MISTAKE: Students may forget to account for the stretching of the bungee cord or incorrectly convert potential energy to kinetic energy, leading to incorrect calculations.