The Physics Behind Trampoline Launch: A Sneaky Teenager's Mischief

Understanding the Physics

Given:
Mass of mother (m) = 79 kg
Initial speed of mother (v) = 2.5 m/s

Explanation:
In this scenario, the sneaky teenager uses a ring attached at the center of the trampoline to pull it down slowly. The mother, with a mass of 79 kg, is on the trampoline while this happens. When the teenager releases the trampoline, the stored energy in the trampoline launches the mother upward.

By analyzing the conservation of energy, we can understand the physics behind the launch. The kinetic energy acquired by the mother comes from the elastic potential energy stored in the trampoline as it was stretched by the teenager pulling it down. This can be calculated by the formula:

Formula:
Elastic Potential Energy = Kinetic Energy of mother
\[ \frac{1}{2}kx^2 = \frac{1}{2}mv^2 \]

Substituting the given values into the formula, we can calculate the elastic potential energy stored in the trampoline:

\[ E = \frac{1}{2} \times 79 \times 2.5^2 = 246.875\,J \]

Therefore, 246.875 joules of energy are stored in the trampoline as the teenager pulls the ring and stretches it down, which then launches the mother upward when released.