A bungee jumper with mass 60.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 49.0 s. He finally comes to rest 30.0 m below the level of the bridge.
1) Calculate the spring constant of the bungee cord.2) Calculate the unstretched length of the bungee cord.

a) Spring constant,k = 63.09 N/m

b) Unstretched length = 20.68 m          

Explanation:

a) Mass of the bungee jumper, M = 60 kg

time for complete oscillation, t = 49 s

Number of oscillations, n = 8

The period of oscillation, T = t/n

T = 49/8

T = 6.125 s

To calculate the spring constant of the bungee cord, use the formula:

Spring constant,k = 63.09 N/m

b) The extension in the spring is given by the formula:

x = mg / K

x = (60*9.8)/63.09

x = 9.32 m

extension, x = final length - original length

Original length = Final length - extension

Original length = 30 - 9.32

Original length = 20.68m                                

Unstretched length = 20.68 m            

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .