Standard +0.8 This is a multi-step energy conservation problem requiring careful consideration of two phases (free fall and elastic extension), setting up a quadratic equation from energy principles, and working with realistic parameters. It's above average difficulty due to the need to identify when the rope becomes taut, account for air resistance throughout, and solve a non-trivial equation, but remains a standard Further Maths mechanics application without requiring novel insight.
A bungee jumper of mass 80 kg steps off a high bridge with an elastic rope attached to her ankles. She is assumed to fall vertically from rest and the air resistance she experiences is modelled as a constant force of 32N. The rope has natural length 4 m and modulus of elasticity of 470 N.
By considering energy, determine the total distance she falls before first coming to instantaneous rest.
[6]
A bungee jumper of mass 80 kg steps off a high bridge with an elastic rope attached to her ankles. She is assumed to fall vertically from rest and the air resistance she experiences is modelled as a constant force of 32N. The rope has natural length 4 m and modulus of elasticity of 470 N.
By considering energy, determine the total distance she falls before first coming to instantaneous rest.
[6]
\hfill \mbox{\textit{SPS SPS FM Mechanics 2022 Q1 [6]}}