Answer:
The maximum distance Charles will push down the trampoline ≈ 0.342 m
Explanation:
The given parameters are;
The mass of the trampoline artist, m = 75 kg
The speed with which the trampoline artist lands, v = 9.0 m/s
The value of the spring constant of the trampoline, k = 52,000 N/m
Let x represents the maximum distance Charles will push down the trampoline
Therefore, we have;
Kinetic energy = 1/2·m·v²
The kinetic energy with which the trampoline artist lands = 1/2 × 75 × 9.0² = 3037.5
The kinetic energy with which the trampoline artist lands = 3037.5 J
The potential energy stored in a spring = 1/2·k·x² = The kinetic energy with which the trampoline artist lands
∴ 1/2 × 52,000 × x² = 3037.5
∴ x = √(3037.5/(1/2 × 52,000)) ≈ 0.342
The maximum distance Charles will push down the trampoline = x ≈ 0.342 m
