Answer:
k = 104.5 N/m
Explanation:
When she reaches the lowest point the velocity of the jumper is 0. This means all her kinetic energy has been absorbed by the cord.
The energy absorbed by a spring (a cord can be treated as a spring when it's being stretched) is:
Where:
Ee = elastic potential energy
k = elastic constant
Δx = lenght the spring was stretched
When a body falls, it's potential gravitational energy is converted to kinetic energy. So the kinetic energy of a body can be calculated as the gravitational potential energy it lost.
The gravitational potential energy is:
Where:
Ep: potential gravitational energy
m: mass
g: acceleration of gravity
Δh: change of height (final - initial)
When she has fallen 31 m she has lost
62 kg * 9.81 m/s^2 * 31 m = 18854 J
Since her velocity at the bottom is 0, her kinetic energy is 0 J.
All her kinetic energy has been absorbed by the cord and transformed into elastic potential energy. So we can equate these two energies.
Ep = Ee
Then:
Δx = 31 m - 12 m = 19 m
From here the only unknown is k: