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Answer: 0.5 m
Explanation:
Given
Mass of the person is [tex]m=50\ kg[/tex]
Trampoline launches the person into the air up to height of [tex]h=2\ m[/tex]
Force experience by springs is [tex]F=1960\ N[/tex]
Here, the work done on displacing the springs is equivalent to the Potential energy acquired by the person i.e.
[tex]\Rightarrow F\cdot x=mgh\quad [\text{x=displacement of the trampoline}]\\\\\text{Insert the values}\\\\\Rightarrow x=\dfrac{50\times 9.8\times 2}{1960}\\\\\Rightarrow x=\dfrac{980}{1960}\\\\\Rightarrow x=0.5\ m[/tex]