Final answer:
The percent of the ball's energy that is dissipated while the ball is in contact with the floor, when h2 is equal to 45h1, is calculated using the conservation of energy principle. After the calculations, the result is 55%, which does not match any of the given options, indicating a possible error in the question or answer choices. Option C is the nearest correct answer.
Step-by-step explanation:
To solve the problem of what percent of the ball's energy is dissipated while the ball is in contact with the floor, given that h2 is equal to 45h1, we can use the conservation of energy principle and relate this to the ball's gravitational potential energy at the peak of its bounces.
Initially, the ball's potential energy at height h1 is PE1 = mgh1, and after the bounce to height h2, it's PE2 = mgh2. Since h2 = 45h1, then PE2 = mg(45h1). To find the percent energy lost, we look at the ratio of energy lost (PE1 - PE2) to the initial potential energy:
Percent Energy Lost = ℓ((PE1 - PE2) / PE1) × 100
Substituting the given values, we find:
Percent Energy Lost = ℓ((mgh1 - mg(45h1)) / mgh1) × 100
Since mass (m) and gravitational acceleration (g) are constants and can be canceled out, we obtain:
Percent Energy Lost = ℓ((1 - 45) / 1) × 100
Percent Energy Lost = 55%
This result is not matching any of the options provided, indicating a possible mistake in the formulation of the question or the answer options. Therefore, none of the options A) 20%, B) 25%, C) 50%, or D) 75% is correct based on the information given.