Question

It's your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 120 m above a raging river and attach a 30-m -long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 45 N/m . Assume that your mass is 71 kg . After a long hesitation, you dive off the bridge.

Part A

How far are you above the water when the cord reaches its maximum elongation?

Express your answer with the appropriate units.

Answer 1

Assume that your mass is (m) = 71 kg

The bungee is 30 long

A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of (k) =45 N/m .

Height above the river is =120m

So, when the person is falling then its a free fall then from the kinematic equations

s =ut+(1/2)gt2

s =(1/2)gt2 for free fall u =0

30 =4.9t2 then t =Sqrt(30/4.9) =2.474s

now the final velocity at this time is given by

v =u+gt

v =(9.81)(2.474) =24.27m/s

Now the kinetic energy at this point is given by

KE =(1/2)mv² =0.5*71*(24.27)² =20910J

At the same point there will be potential energy also

mg(120-30) =71*9.81*90=62686J

After this point the bungee starts to stretch and the energydecreases and at the max elongation the energy is transferred tothe bungee and potential energy depending on your final height.

Therefore

62686+20910 =(1/2)kx² +mgh

As weknow h+x =90 and h =90-x

83596 =(1/2)45*x² +71*9.81(90-x)

22.5x2 -83596+62686-696x=0

22.5x2 -20910-696x =0

solving the above quadratic equation we get x as x =49.650m

How far are you above the water when the cord reaches its maximum elongation is given by

h =90-49.650 =40.350m