I am not so sure about this it is too difficult
The correct answer is b i believe
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)
Speed of wave = Frequency x Wavelength
so Speed = 0.7 x 9 = 6.3
remember the calculations must be done in their Basic SI units.
therefore, you have to convert 7 mm to meters which becomes 0.7 meters