Question

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 spring with spring constant ? = 28.5 N/m – stretches to a new equilibrium with length ?? = 20.0 m (since this is the new equilibrium, let us refer to it as ? = 0 in Hooke’s law and in the elastic potential energy). Note that I have changed the numbers a bit from the ones in class.
After hanging out at this new equilibrium for a bit, Kate starts to get worried. She yells up to her friend Ken, who is frantically trying to figure out how to hoist her back up. After a couple of hours of this, Kate starts to get hungry. She begs Ken to throw her down a backpack full of provisions with mass ? = 15.0 kg. Ken complies, dropping the bag from the bridge with no initial velocity. Throughout this problem you may neglect all sources of friction or other non-conservative forces.

a) Kate catches the bag when it gets to her. What are the momenta of Kate and the bag just before she catches it? What about after?

b) What is the total energy of Kate plus the bag before and after the collision? Is energy conserved during the process of catching the bag?

c) After Kate catches the bag, the bungee cord starts to stretch. What is her downward speed when she hits the river?

d) Sensing her impending doom, Kate thinks fast and strips off her heavy winter coat, which has a mass of 2.00 kg. Just before she's about to go into the river, she throws the coat downward with all her might. With what speed must she throw the coat to avoid drowning?

Answer 1