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Answer :
Avi, the gymnast, should reach a height of approximately 1.41 meters when jumping on the trampoline.
To find the height Avi reaches on the trampoline, we can use the principle of conservation of mechanical energy. The initial potential energy stored in the compressed trampoline is converted into kinetic energy and gravitational potential energy at the highest point of the jump.
The potential energy stored in a spring is given by the equation PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement or compression of the spring. In this case, the trampoline is compressed by 20 cm, which is equivalent to 0.2 meters.
The potential energy stored in the trampoline is then given by PE = (1/2)(176,400 N/m)(0.2 m)² = 3528 J.
At the highest point of the jump, all of the potential energy is converted into gravitational potential energy. The gravitational potential energy is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Substituting the known values, 3528 J = 40 kg * 9.8 m/s² * h. Solving for h, we find h ≈ 1.41 meters.
Therefore, Avi should reach a height of approximately 1.41 meters when jumping on the trampoline.
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