Answer:
Xmax = 0.21 m
Step-by-step explanation:
If X is the maximum compression of the spring and h is the initial height of the spring with respect to its final position, we get:
It means that the block starts with gravitational potential energy and ends with elastic potential energy. So, by the conservation of Energy:

Where m is the mass, g is the gravity and k is the spring constant.
Additionally, h = (d + x)sin30, so we can rewrite the equation as:

So, replacing the values, we get:

Now, using the quadratic equation, we can solve for x:
![\begin{gathered} x=\frac{58.8\pm\sqrt[]{58.8^2-4(2000)(-82.2)}}{2(2000)} \\ x=0.22 \\ or \\ x=-0.19 \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/9rmde2ll0njsw3jq4uv8kpu9knxjv4op2r.png)
Therefore, the maximum compression of the spring will be Xmax = 0.22 m.