Sally weighs 128 lbs and has made decision to bungee of bridge. We will suppose bungee cord acts as the spring. In equilibrium, 144 foot cord stretches additional 640/13 feet. Cord has built-in damping which exerts 80 lbs of force when bungee jumper reaches 100 f/s.
i) When Sally jumps off bridge, cord's elasticity is not being used. Due to freefall only and neglecting wind resistance, find velocity at moment when cord first has tension? Consider t=0 represent first moment of tension, hence this velocity equals y'(0))
ii) Write differential equation which models bungee jump.
iii) Solve the equation. Determine postion function y(t) at anytime t.
iv) Find lowest point, and when she reaches it?