Jose, whose mass is 75 kg, has just completed his first bungee jump and is now bouncing up and down at the end of the cord. His oscillations have an initial amplitude of 11.0 m and a period of 4.0 s.

From what height above the lowest point did Jose jump?

k=185 n/m
Vmax = 17 m/s

To determine the height from which Jose jumped, we can use the concept of energy conservation.

The total mechanical energy of the system is conserved, which is the sum of the potential energy and the kinetic energy.

At the highest point of the oscillation, when Jose momentarily stops before descending, all his potential energy is converted to kinetic energy. At this point, his potential energy is zero and his kinetic energy is maximum.

From the given information, we have the maximum velocity (Vmax) of 17 m/s. The formula for kinetic energy is:

Kinetic Energy = (1/2) * mass * (velocity)^2

We can equate the maximum kinetic energy to the potential energy at the highest point:

(1/2) * mass * (Vmax)^2 = mass * g * height

Here, g is the acceleration due to gravity (9.8 m/s^2). We can rearrange the equation to solve for the height (h):

height = (1/2) * (Vmax^2) / g

Plugging in the given values:

height = (1/2) * (17^2) / 9.8

height = (1/2) * 289 / 9.8

height ≈ 8.31 meters

Therefore, Jose jumped from a height of approximately 8.31 meters above the lowest point.