Final answer:
The kinetic energy of the water balloon at the bottom of its 36 m fall is found using the conservation of energy principle, which equates the initial potential energy to the final kinetic energy, resulting in 774.48 J.
Step-by-step explanation:
To determine the kinetic energy of the water balloon at the bottom of its fall, we can use the principle of conservation of energy. Initially, the balloon has potential energy due to its height above the ground, and this energy is converted to kinetic energy as the balloon falls.
Step-by-step Calculation
- Calculate the initial potential energy (PE) using PE = mgh, where m is mass (2.2 kg), g is the acceleration due to gravity (9.81 m/s2), and h is the height (36 m).
- Since there's no initial kinetic energy (the balloon is dropped from rest), the total mechanical energy at the top equals the potential energy.
- At the bottom, assuming no energy is lost to air resistance, the potential energy at the top is completely transformed into kinetic energy (KE) at the bottom, so KE = PE.
- Substitute the calculated potential energy as the kinetic energy at the bottom of the fall to find the final kinetic energy.
Following this process gives us KE = (2.2 kg)(9.81 m/s2)(36 m) = 774.48 J (rounded to two decimal places).