The launch velocity is 4.8 m/s
Explanation:
We can solve this problem by applying the law of conservation of energy. In fact, the mechanical energy of the hopper (equal to the sum of the potential energy + the kinetic energy) is conserved. So we can write:

where:
 is the initial potential energy, at the bottom
 is the initial potential energy, at the bottom
 is the initial kinetic energy, at the bottom
 is the initial kinetic energy, at the bottom
 is the final potential energy, at the top
 is the final potential energy, at the top
 is the final kinetic energy, at the top
 is the final kinetic energy, at the top
We can rewrite the equation as:

where:
m is the mass of the hopper
 is the acceleration of gravity
 is the acceleration of gravity
 is the initial height
 is the initial height
u is the launch speed of the hopper
 is the maximum altitude reached by the hopper
 is the maximum altitude reached by the hopper
v = 0 is the final speed (which is zero when the hopper reaches the maximum height)
Solving the equation for u, we find the launch speed of the hopper:

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