#### Answer

(a) $h = \frac{k~(\Delta x)^2}{2mg}$
(b) The ice cube goes up to a height of 0.26 m

#### Work Step by Step

(a) The block's potential energy at the maximum height will be equal to the initial energy stored in the spring. We can find an expression for the maximum height $h$;
$PE = U_s$
$mgh = \frac{1}{2}k(\Delta x)^2$
$h = \frac{k~(\Delta x)^2}{2mg}$
(b) We can use the expression from part (a) to find the maximum height $h$;
$h = \frac{k~(\Delta x)^2}{2mg}$
$h = \frac{(25~N/m)(0.10~m)^2}{(2)(0.050~kg)(9.80~m/s^2)}$
$h = 0.26~m$
The ice cube goes up to a height of 0.26 m.