Answer
The cheese will go up to a maximum height of 1.72 meters above its initial position.
Work Step by Step
The potential energy of the cheese at maximum height will be equal to the initial potential energy in the spring.
$U_{grav} = \frac{1}{2}kx^2$
$mgh = \frac{1}{2}kx^2$
$h = \frac{kx^2}{2mg} = \frac{(1800~N/m)(0.150~m)^2}{(2)(1.20~kg)(9.80~m/s^2)}$
$h = 1.72~m$
The cheese will go up to a maximum height of 1.72 meters above its initial position.