Answer:
0.86 m
Explanation:
We can solve the problem by using the law of conservation of energy.
The initial mechanical energy of the flower pot is just gravitational potential energy, given by:
[tex]E_i = U = mgh[/tex]
where
m = 2.50 kg is the mass of the pot
g = 9.8 m/s^2 is the acceleration due to gravity
h = 12.0 m is the height
When the pot hits and compresses the spring coming to a stop, all this energy is converted into elastic potential energy of the spring:
[tex]E_f = U = \frac{1}{2}kx^2[/tex]
where
k = 800 N/m is the spring constant
x is the compression of the spring
Due to the conservation of energy,
[tex]E_i = E_f[/tex]
So we can write
[tex]mgh=\frac{1}{2}kx^2\\x=\sqrt{\frac{2mgh}{k}}=\sqrt{\frac{2(2.50 kg)(9.8 m/s^2)(12.0 m)}{800 N/m}}=0.86 m[/tex]
