Trampoline Stretch Calculation Challenge

How can we determine the distance a trampoline stretches when a gymnast lands on it after jumping to a maximum height? The distance a trampoline stretches when a gymnast lands on it after jumping to a maximum height can be determined by utilizing the principles of Hooke's law and gravitational potential energy.

When a gymnast jumps on a trampoline, the trampoline stretches due to the force exerted by the gymnast's weight. This stretching can be calculated by considering the mass of the gymnast, the maximum height she reaches during the jump, and the minimum displacement of the trampoline when she lands.

Calculating the Displacement:

Given the mass of the gymnast is 51.00 kg, the maximum height reached is 2.100 m, and the minimum displacement of the trampoline is 61.00 cm, we can calculate the displacement using the following formula:

F = kx mg = kx x = mg/k

By considering the gravitational potential energy:

Ug = mgh (1/2)kx_min^2 = mgh k = (2mgh)/(x_min^2)

Substitute the value of k into the equation x = mg/k:

x = (x_min^2)/(2h)

Plugging in the values:

x = (61.00 * 10^-2)/(2 * 2.100) x = 0.1452 m

Therefore, the displacement of the trampoline when the gymnast lands on it is 0.1452 meters.

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