<span>I believe it's insulation.</span>
The elastic potential energy of a spring is given by
![U= \frac{1}{2}kx^2](https://tex.z-dn.net/?f=U%3D%20%5Cfrac%7B1%7D%7B2%7Dkx%5E2%20)
where k is the spring's constant and x is the displacement with respect to the relaxed position of the spring.
The work done by the spring is the negative of the potential energy difference between the final and initial condition of the spring:
![W=-\Delta U = \frac{1}{2}kx_i^2 - \frac{1}{2}kx_f^2](https://tex.z-dn.net/?f=W%3D-%5CDelta%20U%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dkx_i%5E2%20-%20%20%5Cfrac%7B1%7D%7B2%7Dkx_f%5E2%20%20)
In our problem, initially the spring is uncompressed, so
![x_i=0](https://tex.z-dn.net/?f=x_i%3D0)
. Therefore, the work done by the spring when it is compressed until
![x_f](https://tex.z-dn.net/?f=x_f)
is
![W=- \frac{1}{2}kx_f^2](https://tex.z-dn.net/?f=W%3D-%20%5Cfrac%7B1%7D%7B2%7Dkx_f%5E2%20)
And this value is actually negative, because the box is responsible for the spring's compression, so the work is done by the box.
Answer:
Height reached will be 28.35 m
Explanation:
Here we can use the work energy theorem to find the maximum height
As we know by work energy theorem
Work done by gravity + work done by friction = change in kinetic energy
![-mgh - F_f h = 0 - \frac{1}{2}mv_i^2](https://tex.z-dn.net/?f=-mgh%20-%20F_f%20h%20%3D%200%20-%20%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2)
now we will have
![-1.60(9.8)(h) - 0.900(h) = - 470](https://tex.z-dn.net/?f=-1.60%289.8%29%28h%29%20-%200.900%28h%29%20%3D%20-%20470)
![-16.58 h = -470](https://tex.z-dn.net/?f=-16.58%20h%20%3D%20-470)
![h = 28.35 m](https://tex.z-dn.net/?f=h%20%3D%2028.35%20m)
so here the height raised by the stone will be 28.35 m from the ground after projection in upward direction