In class we learned about Kate, a bungee jumper with mass ? =50.0 kg who jumps off a bridge of height ℎ = 25.0 m above a river.After she jumps, the bungee cord – which behaves as an ideal springwith spring constant ? = 28.5 N/m – stretches to a new equilibriumwith length ?? = 20.0 m (since this is the new equilibrium, let usrefer to it as ? = 0 in Hooke’s law and in the elastic potentialenergy). Note that I have changed the numbers a bit from the onesin class.
After hanging out at this new equilibrium for a bit, Kate starts toget worried. She yells up to her friend Ken, who is franticallytrying to figure out how to hoist her back up. After a couple ofhours of this, Kate starts to get hungry. She begs Ken to throw herdown a backpack full of provisions with mass ? = 15.0 kg. Kencomplies, dropping the bag from the bridge with no initialvelocity. Throughout this problem you may neglect all sources offriction or other non-conservative forces.
a) Kate catches the bag when it gets to her. What are themomenta of Kate and the bag just before she catches it? What aboutafter?
b) What is the total energy of Kate plus the bag before andafter the collision? Is energy conserved during the process ofcatching the bag?
c) After Kate catches the bag, the bungee cord starts tostretch. What is her downward speed when she hits the river?
d) Sensing her impending doom, Kate thinks fast and strips offher heavy winter coat, which has a mass of 2.00 kg. Just beforeshe's about to go into the river, she throws the coat downward withall her might. With what speed must she throw the coat to avoiddrowning?
