Question

An object falls from a height of 10 m above the ground. After striking the ground it loses $50\%$ of its kinetic energy. The height upto which the object can rebounce from the ground is:

• A. 7.5 m
• B. 10 m
• C. 2.5 m
• D. 5 m

Answer 1

The Correct Option is D

1. Initial Potential Energy: The initial potential energy (PE) is calculated as mgh, where m represents mass, g denotes the acceleration due to gravity, and h is the starting height, which is 10 m.

2. Kinetic Energy Before Impact: Due to the conservation of energy, the potential energy transforms into kinetic energy (KE) immediately preceding impact with the ground. Therefore, KE = mgh.

3. Kinetic Energy After Impact: Following the ground impact, the object retains 50% of its initial KE. The remaining KE is thus 0.5(mgh).

4. Rebound Height Calculation: The residual KE is converted back into potential energy during the object's rebound. Designating h’ as the rebound height, we have 0.5(mgh) = mgh’. Solving for h’ yields h’ = 0.5h, which equates to 0.5(10 m) = 5 m.

5. Outcome: The object rebounds to a height of 5 m.