Calculating Trampoline Stretch Distance After Ball Impact

Explanation:

To determine how far the ball will stretch the trampoline after impact, we can use conservation of energy principles. The potential energy (PE) at the start of the fall will be converted to elastic potential energy (EPE) when the trampoline is stretched to its maximum.

The potential energy of the 2kg ball at a height of 5m is given by PE = mgh, where mass m = 2kg, acceleration due to gravity g = 9.8m/s², and height h = 5m. PE = 2kg * 9.8m/s² * 5m = 98 Joules.

To find the stretch (x) in the trampoline using the spring constant (k = 1000 N/m), we set this equal to the elastic potential energy, which is given by EPE = 1/2 * k * x². We have:

98 J = 1/2 * 1000 N/m * x²
x² = 98 J * 2 / 1000 N/m
x² = 0.196 m²
x = sqrt(0.196 m²)
x ≈ 0.44 m

Therefore, the trampoline will stretch approximately 0.44 meters after impact.