Answer:
The vertical distance is ![d = \frac{2}{k} *[mg + f]](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B2%7D%7Bk%7D%20%2A%5Bmg%20%2B%20f%5D)
Explanation:
From the question we are told that
The mass of the cylinder is m
The kinetic frictional force is f
Generally from the work energy theorem

Here E the the energy of the spring which is increasing and this is mathematically represented as

Here k is the spring constant
P is the potential energy of the cylinder which is mathematically represented as

And
is the workdone by friction which is mathematically represented as

So

=> ![\frac{1}{2} * k * d^2 = d[mg + f ]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%5E2%20%3D%20%20d%5Bmg%20%2B%20%20f%20%20%20%20%5D)
=> ![\frac{1}{2} * k * d = [mg + f ]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%20%3D%20%20%5Bmg%20%2B%20%20f%20%20%20%20%5D)
=> ![d = \frac{2}{k} *[mg + f]](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B2%7D%7Bk%7D%20%2A%5Bmg%20%2B%20f%5D)
The question is missing, but I guess the problem is asking for the distance between the cliff and the source of the sound.
First of all, we need to calculate the speed of sound at temperature of

:

The sound wave travels from the original point to the cliff and then back again to the original point in a total time of t=4.60 s. If we call L the distance between the source of the sound wave and the cliff, we can write (since the wave moves by uniform motion):

where v is the speed of the wave, 2L is the total distance covered by the wave and t is the time. Re-arranging the formula, we can calculate L, the distance between the source of the sound and the cliff:
W = 1/2k*x^2.
k = spring constant = 2500 n/m.
x = distance = 4 cm = 0.04m (convert to same units).
W = 1/2(2500)(0.04)^2 = 2J.
Combine all of the x's on one side of the equation and then finish the problem!