Conservation Of Energy

Step 1: Understanding the Concept:
Use the work-energy theorem: The loss in potential energy equals the gain in kinetic energy plus the energy lost due to air resistance.

Step 2: Detailed Explanation:
Mass, . Height, . Initial velocity, . Energy loss due to air resistance, . Initial potential energy, . Final kinetic energy, . By energy conservation:

Step 3: Final Answer:
The velocity on striking the ground is .

Step 1: Understanding the Concept:
When a ball falls from an initial height and bounces back up to a lower final height, it has lost a portion of its initial mechanical energy.
This energy loss is typically due to non-conservative forces like air resistance and the inelastic nature of the collision with the ground.
Step 2: Key Formula or Approach:
The potential energy of the ball at any given height is .
The percentage loss of energy is calculated using the formula:
Step 3: Detailed Explanation:
Let the initial height be .
Let the final height reached after the bounce be .
The initial potential energy before falling is .
The final potential energy after the bounce is .
The loss in energy is .
Substituting the values, the percentage energy loss is:
Step 4: Final Answer:
The percentage loss of energy is .