Bungee Jumper: Calculating Maximum Velocity

What is the maximum velocity of a bungee jumper?

A bungee jumper of mass 50kg is attached to a bungee with a constant of 100Nm. The unstretched length of the bungee is 15m.

Answer:

The maximum velocity of the jumper is 18.5 m/s.

The maximum velocity of a bungee jumper can be calculated by equating the jumper's initial gravitational potential energy to their kinetic energy at terminal velocity. We use the formulas for potential and kinetic energy to perform this calculation.

Explanation:

The maximum velocity of the jumper, known as terminal velocity, can be found by applying the conservation of energy. Initially, at the top of the jump, the jumper has gravitational potential energy but no kinetic energy. When the jumper starts falling, their potential energy converts to kinetic energy, which affects their velocity.

We know the gravitational potential energy at the top of the jump can be given by P.E. = m*g*h where m is the mass (50 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the jump takes place. The exact height in this scenario isn't given, but if we assume it's the unstretched bungee length (15m), then P.E. = 50kg * 9.8m/s² * 15m = 7350 Joules.

This gravitational potential energy will be completely converted to kinetic energy at the maximum speed of the jumper. Therefore, we can write K.E. = P.E. Hence, at terminal velocity, K.E. = 0.5*m*v², which gives us v² = (2*7350)/50. Solving for v gives the max velocity.