This question involves the concepts of the law of conservation of energy, gravitational potential energy, and elastic potential energy.
The total distance travelled up by the ice cube is "51 cm".
Applying the law of conservation of energy in this situation gives us:
[tex]Elastic\ Potential\ Energy\ Lost = Gravitataional\ Potential\ Energy\ Gained\\\\\frac{1}{2}kx^2=mgh\\[/tex]
where,
k = spring constant = 25 N/m
x = compression = 10 cm = 0.1 m
m = mass of cube = 50 g = 0.05 kg
g = acceleration due to gravity = 9.81 m/s²
h = height gained = ?
Therefore,
[tex]\frac{1}{2}(25\ N/m)(0.1\ m)^2=(0.05\ kg)(9.81\ m/s^2)h\\\\h = \frac{0.125}{0.4905}\\\\h = 0.255\ m = 25.5\ cm[/tex]
Now, we will use trigonometric ratios to find out the distance travelled by the cube on the slope (d):
[tex]Sin\ 30^o=\frac{Perpendicular}{Hypotenuse}=\frac{h}{d}\\\\Sin\ 30^o=\frac{25.5\ cm}{d}\\\\d = \frac{25.5\ cm}{Sin\ 30^o}\\\\[/tex]
d = 51 cm
Learn more about the law of conservation of energy here:
brainly.com/question/20971995?referrer=searchResults
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