A daredevil plans to bungee jump from a balloon 64.0 m above a carnival midway. He will use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 10.0 m above the ground. Model his body as a particle and the cord as having negligible mass and obeying Hooke's law. In a preliminary test, hanging at rest from a 5.00 m length of the cord, he finds that his body weight stretches it by 1.60 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon.

and the question is?

The question is : (a) what is the lenght of the cord he should use (b) what is the maximum acceleration he will experience

To solve this problem, we need to determine the properties of the elastic cord and calculate the length of the cord attached to the stationary balloon.

Let's first define some variables:
- The length of the cord attached to the balloon (unknown) = L
- The length of the cord during the preliminary test = L₀ (given as 5.00 m)
- The decrease in length during the preliminary test = ΔL (given as 1.60 m)
- The initial position of the daredevil = h_initial (given as 64.0 m)
- The final position of the daredevil = h_final (given as 10.0 m)
- The gravitational acceleration = g (approximately 9.8 m/s²)

Using Hooke's law for an elastic cord, which states F = -k * ΔL, where F is the force, k is the spring constant, and ΔL is the change in length, we can find the spring constant of the cord during the preliminary test:
F₀ = -k * ΔL₀

In this case, the force F₀ is equal to the weight of the daredevil. Therefore:
F₀ = mass * g

Since we are modeling the daredevil as a particle, we can assume his mass is concentrated at a single point. So:
F₀ = m * g

Now we need to calculate the spring constant k:
k = -F₀ / ΔL₀

Now that we have the spring constant, we can determine the length of the cord attached to the balloon, L, using a proportion equation:

(L - L₀) / L₀ = (h_initial - h_final) / L₀

Simplifying, we get:
L - L₀ = (h_initial - h_final)

Finally, solving for L:
L = L₀ + (h_initial - h_final)

Substituting the given values, we can find the answer.