Answer to Question #86977 in Mechanics | Relativity for Maria

Question

Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, (Figure 1). He falls for 15 m before the bungee cord begins to stretch. Chris's mass is 80 kg and we assume the cord obeys Hooke's law, F=−kx, with 54 N/m.
If we neglect air resistance, estimate what distance d below the bridge Chris's foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle.
Express your answer to two significant figures and include the appropriate units.

Answer 1

From the conservation of energy:

$$mg(h+x)=0.5kx^2$$

$$80(9.8)(15+x)=0.5(54)x^2$$

$$x = 40 m.$$

The distance d below the bridge:

$$d=x+h=40+15=55 m.$$