A 500 g ball is released from a height of 4m. Each time it makes contact with the ground, it loses 25% of its kinetic energy. Find the kinetic energy it possess just after the `3^(rd)` hit

Options

A. 15 J
B. 11.25 J
C. 8.44 J
D. none of these

Answer

To find the kinetic energy possessed by the ball just after the third hit, we can follow these steps:

### Step 1: Calculate the initial potential energy (PE) of the ball
The potential energy when the ball is at a height \( h \) can be calculated using the formula:
\[ PE = mgh \]
where:
- \( m = 500 \, \text{g} = 0.5 \, \text{kg} \) (mass of the ball),
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity),
- \( h = 4 \, \text{m} \) (height from which the ball is released).

Substituting the values:
\[ PE = 0.5 \times 9.8 \times 4 = 19.6 \, \text{Joules} \]

### Step 2: Determine the kinetic energy just before the first hit
When the ball is released, all the potential energy converts to kinetic energy just before the first hit:
\[ KE_0 = PE = 19.6 \, \text{Joules} \]

### Step 3: Calculate the kinetic energy after the first hit
The ball loses 25% of its kinetic energy upon hitting the ground, meaning it retains 75% of its kinetic energy:
\[ KE_1 = KE_0 \times \left(1 - 0.25\right) = KE_0 \times 0.75 \]
Substituting the value:
\[ KE_1 = 19.6 \times 0.75 = 14.7 \, \text{Joules} \]

### Step 4: Calculate the kinetic energy after the second hit
Applying the same logic, after the second hit, the ball again retains 75% of its kinetic energy:
\[ KE_2 = KE_1 \times 0.75 \]
Substituting the value:
\[ KE_2 = 14.7 \times 0.75 = 11.025 \, \text{Joules} \]

### Step 5: Calculate the kinetic energy after the third hit
Finally, after the third hit, the ball retains 75% of its kinetic energy:
\[ KE_3 = KE_2 \times 0.75 \]
Substituting the value:
\[ KE_3 = 11.025 \times 0.75 = 8.26875 \, \text{Joules} \]

### Step 6: Round the answer
Rounding the final result gives:
\[ KE_3 \approx 8.27 \, \text{Joules} \]

### Final Answer
The kinetic energy possessed by the ball just after the third hit is approximately **8.27 Joules**.

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