Final answer:
The bungee cord required for a 100m jump should have an unstretched length of 83.33m to ensure the bungee jumper stops at river level. Following oscillations, the jumper comes to rest at the river level. The period of oscillations depends on the jumper's mass and the spring constant of the cord, calculable by T = 2π√(m/k).
Step-by-step explanation:
Bungee Jumping Physics Problem
To solve this physics problem, apply principles of elasticity, harmonic motion, and energy conservation. Given that the bungee cord stretches 20% when the jumper hangs from it, the length of bungee cord required to stop exactly at river level for a 100m jump is found by considering that after stretching by 20%, the new length will be 120% of the original length (L). This implies that 1.2L = 100m, leading to L = ∙m (a). The height above the river where the jumper will end up after oscillations should be zero as energy loss mechanisms, such as air resistance, will damp the motion until the jumper comes to rest at the lowest point (b). To find the period of small amplitude oscillations, use the formula for the period (T) of a mass on a spring, T = 2π√(m/k), where m is the mass and k is the spring constant of the bungee cord (c).
The specifics of the jumper's mass and the exact spring constant are necessary to precisely solve for the period of oscillation. However, this formula provides the general approach to the eventual calculation.