Trampoline Performer: Finding Speed and Compression Distance

How can we determine the speed of a trampoline performer as he impacts the trampoline?

How far will the trampoline be compressed when the performer lands on it?

Answer:

The speed of the trampoline performer as he impacts the trampoline is 7.0 m/s, and the compression distance of the trampoline is 0.106 m.

To find the speed of the trampoline performer as he impacts the trampoline, we can use the principle of conservation of energy. The initial potential energy of the performer is determined by his height above the trampoline, while the final kinetic energy is determined by his speed.

Since the trampoline behaves like a spring with a spring constant of 6.2 x 10⁴ N/m, we can calculate the compression distance using Hooke's Law.

Speed of the performer:

Initial potential energy: mgh = (65.0 kg)(9.8 m/s²)(3.00 m)

Final kinetic energy: (1/2)mv² = (1/2)(65.0 kg)v²

By setting the two equations equal to each other and solving for v, we find that the speed of the performer is 7.0 m/s.

Compression distance of the trampoline:

Using Hooke's Law (F = kx), we can calculate the compression distance of the trampoline when the performer lands on it. The compression distance is found to be 0.106 m.